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Relevant bibliographies by topics / Linear topological vector space

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Academic literature on the topic 'Linear topological vector space'

Author: Grafiati

Published: 4 June 2021

Last updated: 6 February 2022

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Journal articles on the topic "Linear topological vector space"

1

Khurana, Surjit Singh. "Vector Measures on Topological Spaces." gmj 14, no. 4 (December 2007): 687–98. http://dx.doi.org/10.1515/gmj.2007.687.

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Abstract Let 𝑋 be a completely regular Hausdorff space, 𝐸 a quasi-complete locally convex space, 𝐶(𝑋) (resp. 𝐶𝑏(𝑋)) the space of all (resp. all, bounded), scalar-valued continuous functions on 𝑋, and 𝐵(𝑋) and 𝐵0(𝑋) be the classes of Borel and Baire subsets of 𝑋. We study the spaces 𝑀𝑡(𝑋,𝐸), 𝑀 τ (𝑋,𝐸), 𝑀 σ (𝑋,𝐸) of tight, τ-smooth, σ-smooth, 𝐸-valued Borel and Baire measures on 𝑋. Using strict topologies, we prove some measure representation theorems of linear operators between 𝐶𝑏(𝑋) and 𝐸 and then prove some convergence theorems about integrable functions. Also, the Alexandrov's theorem is extended to the vector case and a representation theorem about the order-bounded, scalar-valued, linear maps from 𝐶(𝑋) is generalized to the vector-valued linear maps.

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Katsaras, A. K., and V. Benekas. "Sequential Convergence in Topological Vector Spaces." gmj 2, no. 2 (April 1995): 151–64. http://dx.doi.org/10.1515/gmj.1995.151.

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Abstract For a given linear topology τ, on a vector space E, the finest linear topology having the same τ convergent sequences, and the finest linear topology on E having the same τ precompact sets, are investigated. Also, the sequentially bornological spaces and the sequentially barreled spaces are introduced and some of their properties are studied.

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García-Pacheco, Francisco Javier, and Francisco Javier Pérez-Fernández. "Pre-Schauder Bases in Topological Vector Spaces." Symmetry 11, no. 8 (August 9, 2019): 1026. http://dx.doi.org/10.3390/sym11081026.

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A Schauder basis in a real or complex Banach space X is a sequence ( e n ) n ∈ N in X such that for every x ∈ X there exists a unique sequence of scalars ( λ n ) n ∈ N satisfying that x = ∑ n = 1 ∞ λ n e n . Schauder bases were first introduced in the setting of real or complex Banach spaces but they have been transported to the scope of real or complex Hausdorff locally convex topological vector spaces. In this manuscript, we extend them to the setting of topological vector spaces over an absolutely valued division ring by redefining them as pre-Schauder bases. We first prove that, if a topological vector space admits a pre-Schauder basis, then the linear span of the basis is Hausdorff and the series linear span of the basis minus the linear span contains the intersection of all neighborhoods of 0. As a consequence, we conclude that the coefficient functionals are continuous if and only if the canonical projections are also continuous (this is a trivial fact in normed spaces but not in topological vector spaces). We also prove that, if a Hausdorff topological vector space admits a pre-Schauder basis and is w * -strongly torsionless, then the biorthogonal system formed by the basis and its coefficient functionals is total. Finally, we focus on Schauder bases on Banach spaces proving that every Banach space with a normalized Schauder basis admits an equivalent norm closer to the original norm than the typical bimonotone renorming and that still makes the basis binormalized and monotone. We also construct an increasing family of left-comparable norms making the normalized Schauder basis binormalized and show that the limit of this family is a right-comparable norm that also makes the normalized Schauder basis binormalized.

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Yılmaz, Yılmaz, Sümeyye Çakan, and Şahika Aytekin. "Topological Quasilinear Spaces." Abstract and Applied Analysis 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/951374.

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We introduce, in this work, the notion of topological quasilinear spaces as a generalization of the notion of normed quasilinear spaces defined by Aseev (1986). He introduced a kind of the concept of a quasilinear spaces both including a classical linear spaces and also nonlinear spaces of subsets and multivalued mappings. Further, Aseev presented some basic quasilinear counterpart of linear functional analysis by introducing the notions of norm and bounded quasilinear operators and functionals. Our investigations show that translation may destroy the property of being a neighborhood of a set in topological quasilinear spaces in contrast to the situation in topological vector spaces. Thus, we prove that any topological quasilinear space may not satisfy the localization principle of topological vector spaces.

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Maslyuchenko, V. K., and V. V. Nesterenko. "Weak Darboux property and transitivity of linear mappings on topological vector spaces." Carpathian Mathematical Publications 5, no. 1 (June 20, 2013): 79–88. http://dx.doi.org/10.15330/cmp.5.1.79-88.

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It is shown that every linear mapping on topological vector spaces always has weak Darboux property, therefore, it is continuous if and only if it is transitive. For finite-dimensional mapping $f$ with values in Hausdorff topological vector space the following conditions are equivalent: (i) $f$ is continuous; (ii) graph of $f$ is closed; (iii) kernel of $f$ is closed; (iv) $f$ is transition map.

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VILLENA, A. R. "UNIQUENESS OF THE TOPOLOGY ON SPACES OF VECTOR-VALUED FUNCTIONS." Journal of the London Mathematical Society 64, no. 2 (October 2001): 445–56. http://dx.doi.org/10.1112/s0024610701002423.

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Let Ω be a topological space without isolated points, let E be a topological linear space which is continuously embedded into a product of countably boundedly generated topological linear spaces, and let X be a linear subspace of C(Ω, E). If a ∈ C(Ω) is not constant on any open subset of Ω and aX ⊂ X, then it is shown that there is at most one F-space topology on X that makes the multiplication by a continuous. Furthermore, if [Ufr ] is a subset of C(Ω) which separates strongly the points of Ω and [Ufr ]X ⊂ X, then it is proved that there is at most one F-space topology on X that makes the multiplication by a continuous for each a ∈ [Ufr ].These results are applied to the study of the uniqueness of the F-space topology and the continuity of translation invariant operators on the Banach space L1(G, E) for a noncompact locally compact group G and a Banach space E. Furthermore, the problems of the uniqueness of the F-algebra topology and the continuity of epimorphisms and derivations on F-algebras and some algebras of vector-valued functions are considered.

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Nakasho, Kazuhisa, Yuichi Futa, and Yasunari Shidama. "Topological Properties of Real Normed Space." Formalized Mathematics 22, no. 3 (September 1, 2014): 209–23. http://dx.doi.org/10.2478/forma-2014-0024.

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Summary In this article, we formalize topological properties of real normed spaces. In the first part, open and closed, density, separability and sequence and its convergence are discussed. Then we argue properties of real normed subspace. Then we discuss linear functions between real normed speces. Several kinds of subspaces induced by linear functions such as kernel, image and inverse image are considered here. The fact that Lipschitz continuity operators preserve convergence of sequences is also refered here. Then we argue the condition when real normed subspaces become Banach’s spaces. We also formalize quotient vector space. In the last session, we argue the properties of the closure of real normed space. These formalizations are based on [19](p.3-41), [2] and [34](p.3-67).

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García-Pacheco, Francisco Javier, Soledad Moreno-Pulido, Enrique Naranjo-Guerra, and Alberto Sánchez-Alzola. "Non-Linear Inner Structure of Topological Vector Spaces." Mathematics 9, no. 5 (February 25, 2021): 466. http://dx.doi.org/10.3390/math9050466.

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Inner structure appeared in the literature of topological vector spaces as a tool to characterize the extremal structure of convex sets. For instance, in recent years, inner structure has been used to provide a solution to The Faceless Problem and to characterize the finest locally convex vector topology on a real vector space. This manuscript goes one step further by settling the bases for studying the inner structure of non-convex sets. In first place, we observe that the well behaviour of the extremal structure of convex sets with respect to the inner structure does not transport to non-convex sets in the following sense: it has been already proved that if a face of a convex set intersects the inner points, then the face is the whole convex set; however, in the non-convex setting, we find an example of a non-convex set with a proper extremal subset that intersects the inner points. On the opposite, we prove that if a extremal subset of a non-necessarily convex set intersects the affine internal points, then the extremal subset coincides with the whole set. On the other hand, it was proved in the inner structure literature that isomorphisms of vector spaces and translations preserve the sets of inner points and outer points. In this manuscript, we show that in general, affine maps and convex maps do not preserve inner points. Finally, by making use of the inner structure, we find a simple proof of the fact that a convex and absorbing set is a neighborhood of 0 in the finest locally convex vector topology. In fact, we show that in a convex set with internal points, the subset of its inner points coincides with the subset of its internal points, which also coincides with its interior with respect to the finest locally convex vector topology.

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Park, Sehie. "Best approximation theorems for composites of upper semicontinuous maps." Bulletin of the Australian Mathematical Society 51, no. 2 (April 1995): 263–72. http://dx.doi.org/10.1017/s000497270001409x.

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Let (E, τ) be a Hausdorff topological vector space and (X, ω) a weakly compact convex subset of E with the relative weak topology ω. Recently, there have appeared best approximation and fixed point theorems for convex-valued upper semicontinuous maps F: (X, ω) → 2(E, τ) whenever (E, τ) is locally convex. In this paper, these results are extended to a very broad class of multifunctions containing composites of acyclic maps in a topological vector space having sufficiently many linear functionals. Moreover, we also obtain best approximation theorems for classes of multifunctions defined on approximatively compact convex subsets of locally convex Hausdorff topological vector spaces or closed convex subsets of Banach spaces with the Oshman property.

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Hejazian, Shirin, Madjid Mirzavaziri, and Omid Zabeti. "Bounded operators on topological vector spaces and their spectral radii." Filomat 26, no. 6 (2012): 1283–90. http://dx.doi.org/10.2298/fil1206283h.

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In this paper, we consider three classes of bounded linear operators on a topological vector space with respect to three different topologies which are introduced by Troitsky. We obtain some properties for the spectral radii of a linear operator on a topological vector space. We find some sufficient conditions for the completeness of these classes of operators. Finally, as a special application, we deduce some sufficient conditions for invertibility of a bounded linear operator.

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Dissertations / Theses on the topic "Linear topological vector space"

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Nielsen, Mark J. "Tilings of topological vector spaces /." Thesis, Connect to this title online; UW restricted, 1990. http://hdl.handle.net/1773/5763.

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Vera, Mendoza Rigoberto. "Linear operations on locally convex topological vector spaces." Diss., The University of Arizona, 1994. http://hdl.handle.net/10150/186699.

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Our purpose is to extend, to the class of linear operators on a locally convex space, some of the results of spectral theory. In order to do this we had to introduce some topologies on the space of operators that are not locally convex. These topologies are of interest in their own right, and have proved useful in enabling us to attain our goal. There is an important class of topological vector spaces named ab-spaces (almost bornological spaces), but there are not too many facts about them. We briefly discuss some new results and give a characterization of those spaces in Chapter 3.

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Toolan, Timothy M. "Advances in sliding window subspace tracking /." View online ; access limited to URI, 2005. http://0-wwwlib.umi.com.helin.uri.edu/dissertations/dlnow/3206257.

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Ramsey, John Karl. "Vector-space implementation of Hamilton's law of varying action for linear and nonlinear systems /." The Ohio State University, 2000. http://rave.ohiolink.edu/etdc/view?acc_num=osu1488196234909189.

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Rees, Michael K. "Topological uniqueness results for the special linear and other classical Lie Algebras." Thesis, University of North Texas, 2001. https://digital.library.unt.edu/ark:/67531/metadc3000/.

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Suppose L is a complete separable metric topological group (ring, field, etc.). L is topologically unique if the Polish topology on L is uniquely determined by its underlying algebraic structure. More specifically, L is topologically unique if an algebraic isomorphism of L with any other complete separable metric topological group (ring, field, etc.) induces a topological isomorphism. A local field is a locally compact topological field with non-discrete topology. The only local fields (up to isomorphism) are the real, complex, and p-adic numbers, finite extensions of the p-adic numbers, and fields of formal power series over finite fields. We establish the topological uniqueness of the special linear Lie algebras over local fields other than the complex numbers (for which this result is not true) in the context of complete separable metric Lie rings. Along the way the topological uniqueness of all local fields other than the field of complex numbers is established, which is derived as a corollary to more general principles which can be applied to a larger class of topological fields. Lastly, also in the context of complete separable metric Lie rings, the topological uniqueness of the special linear Lie algebra over the real division algebra of quaternions, the special orthogonal Lie algebras, and the special unitary Lie algebras is proved.

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Fontenele, Francisca ClÃudia Fernandes. "Fedathi sequence in teaching of linear algebra: the case of the concept of base of a vector space." Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=11351.

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FundaÃÃo Cearense de Apoio ao Desenvolvimento Cientifico e TecnolÃgico
This research examined the teaching of concept of base of a vector space according to the premises mediated by Fedathi Sequence during the discipline âIntroduction to Algebraâ in the course of Engineering of Teleinformatic at Federal University of CearÃ. The objective was to determine whether the use of Fedathi Sequence specifically in classes about the concept of base provides resources capable of becoming Meta Lever, allowing students an education based on the reflection on the worked contents. In this sense, the investigation was conducted in the form of case study, having as subject the teacher of discipline, which allowed the observation during his classes and planning, as well as having granted an interview. The results indicated that the Fedathi Sequence favored the use of resources that could become Meta Lever for students, being decisive in mediating the teacher, once the teacher behavior to use it in the classroom motivates students to reflection. We consider theories ML and FS, in this research, are complementary, and therefore we indicate that the teacher know such tools and their potential for use in teaching of concept of base, awakening the teacher an awareness of the role of mediation suggested by Fedathi Sequence.
Esta pesquisa analisou o ensino da noÃÃo de base de um espaÃo vetorial mediado segundo os pressupostos da SequÃncia Fedathi durante a disciplina de IntroduÃÃo Ã Ãlgebra do curso de Engenharia de TeleinformÃtica da Universidade Federal do CearÃ. Objetivou-se verificar se o uso da SequÃncia Fedathi, especificamente, nas aulas sobre o conceito de base, proporciona recursos passÃveis de se tornarem Alavanca Meta, permitindo aos alunos um ensino baseado na reflexÃo sobre os conteÃdos trabalhados. Nesse sentido, a investigaÃÃo foi conduzida na forma de estudo de caso, tendo como sujeito o professor da disciplina, que permitiu a observaÃÃo durante suas aulas e planejamentos, alÃm de ter concedido uma entrevista. Os resultados encontrados apontaram que a SequÃncia Fedathi favoreceu o uso de recursos passÃveis de se tornarem Alavancas Meta para os alunos, sendo determinante na mediaÃÃo do professor, de modo que a postura docente ao utilizÃ-la em sala de aula motivava os alunos Ã reflexÃo. Consideramos que as teorias AM e SF, nessa pesquisa, se complementaram, e, portanto, indicamos que o professor conheÃa tais ferramentas e seu potencial de uso no ensino de base, despertando no professor uma consciÃncia do papel da mediaÃÃo preconizada pela SequÃncia Fedathi.

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Stover, Derrick D. "Continuous Mappings and Some New Classes of Spaces." View abstract, 2009. http://gateway.proquest.com/openurl?url_ver=Z39.88-2004&res_dat=xri:pqdiss&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&rft_dat=xri:pqdiss:3371579.

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Lima, Diego Ponciano de Oliveira. "Variedades afins e aplicaÃÃes." Universidade Federal do CearÃ, 2013. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=10665.

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In this paper, we consider affine varieties in vector space to analyze and understand the geometric behavior of sets solutions of systems of linear equations, solutions of linear ordinary differential equations of second order resulting from mathematical modeling of systems, etc. We observed characteristics of affine varieties in vector spaces as a subspaces vector transferred to any vector belonging to affine variety and do a comparison of geometric representations of the solution sets of problem situations, cited above, with such features.
Neste trabalho, consideramos variedades afins no espaÃo vetorial para analisar e compreender o comportamento geomÃtrico de conjuntos soluÃÃes de sistemas de equaÃÃes lineares, de soluÃÃes de equaÃÃes diferenciais ordinÃrias lineares de segunda ordem resultantes de modelagens matemÃticas de sistemas, etc. Verificamos caracterÃsticas das variedades afins em espaÃos vetoriais como um subespaÃo vetorial transladado de qualquer vetor pertencente Ã variedade afim e fazemos uma comparaÃÃo das representaÃÃes geomÃtricas dos conjuntos soluÃÃes das situaÃÃes-problema, citados acima, com tais caracterÃsticas.

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"Some sort of barrelledness in topological vector spaces." Chinese University of Hong Kong, 1990. http://library.cuhk.edu.hk/record=b5886544.

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by Kin-Ming Liu.
Thesis (M.Phil.)--Chinese University of Hong Kong, 1990.
Bibliography: leaves 66-67.
Chapter §0 --- Introduction
Chapter §1 --- Preliminaries and notations
Chapter §2 --- A summary on ultra-(DF)-spaces and order-ultra-（DF)-spaces
Chapter §3 --- " ""Dual"" properties between projective and inductive topologies in topological vector spaces"
Chapter §4 --- Application of barrelledness on continuity of bilinear mappings and projective tensor product
Chapter §5 --- Countably order-quasiultrabarrelled spaces

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Helmstedt, Janet Margaret. "Closed graph theorems for locally convex topological vector spaces." Thesis, 2015. http://hdl.handle.net/10539/18010.

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A Dissertation Submitted of the Faculty of Science, University of the Witwatersrand, Johannesburg in Partial Fulfilment of the Requirements for the Degree of Master of Science
Let 4 be the class of pairs of loc ..My onvex spaces (X,V) “h ‘ch are such that every closed graph linear ,pp, 1 from X into V is continuous. It B is any class of locally . ivex l.ausdortf spaces. let & w . (X . (X.Y) e 4 for ,11 Y E B). " ‘his expository dissertation, * (B) is investigated, firstly i r arbitrary B . secondly when B is the class of C,-complete paces and thirdly whon B is a class of locally convex webbed s- .ces

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Books on the topic "Linear topological vector space"

1

1940-, Beckenstein Edward, ed. Topological vector spaces. New York: M. Dekker, 1985.

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Narici, Lawrence. Topological vector spaces. 2nd ed. Boca Raton, FL: CRC Press, 2011.

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Schaefer, Helmut H. Topological vector spaces. 2nd ed. New York: Springer, 1999.

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Nicolas Bourbaki. Topological vector spaces. Berlin: Springer-Verlag, 1987.

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1940-, Beckenstein Edward, ed. Topological vector spaces. 2nd ed. Boca Raton: Taylor & Francis, 2011.

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Wong, Yau-Chuen. Introductory theory of topological vector spaces. New York: Dekker, 1992.

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Introductory theory of topological vector spaces. New York: Dekker, 1992.

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Horváth, John. Topological vector spaces and distributions. Mineola, N.Y: Dover Publications, 2012.

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Topological vector spaces and distributions. Mineola, N.Y: Dover Publications, 2012.

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10

Kadelburg, Zoran. Subspaces and quotients of topological and ordered vector spaces. Novi Sad: University of Novi Sad, Institute of Mathematics, 1997.

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Book chapters on the topic "Linear topological vector space"

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Schaefer, H. H., and M. P. Wolff. "Linear Mappings." In Topological Vector Spaces, 73–121. New York, NY: Springer New York, 1999. http://dx.doi.org/10.1007/978-1-4612-1468-7_4.

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Bourbaki, Nicolas. "Spaces of continuous linear mappings." In Topological Vector Spaces, 127–76. Berlin, Heidelberg: Springer Berlin Heidelberg, 2003. http://dx.doi.org/10.1007/978-3-642-61715-7_3.

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Grosse-Erdmann, Karl-G., and Alfred Peris Manguillot. "Linear dynamics in topological vector spaces." In Universitext, 331–50. London: Springer London, 2011. http://dx.doi.org/10.1007/978-1-4471-2170-1_12.

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Tikhomirov, V. M. "On the Linear Dimension of Topological Vector Spaces." In Selected Works of A. N. Kolmogorov, 388–92. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-3030-1_57.

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Rao, K. N. Srinivasa. "Linear Vector Space." In Texts and Readings in Physical Sciences, 39–122. Gurgaon: Hindustan Book Agency, 2006. http://dx.doi.org/10.1007/978-93-86279-32-3_3.

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Shah, Nita H., and Urmila B. Chaudhari. "Linear Transformations of Euclidean Vector Space." In Linear Transformation, 1–13. First edition. | Boca Raton : CRC Press, 2021. |: CRC Press, 2020. http://dx.doi.org/10.1201/9781003105206-1.

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Lee, Gue Myung, and Sangho Kum. "Vector Variational Inequalities in a Hausdorff Topological Vector Space." In Vector Variational Inequalities and Vector Equilibria, 307–20. Boston, MA: Springer US, 2000. http://dx.doi.org/10.1007/978-1-4613-0299-5_17.

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Romano, Antonio, and Addolorata Marasco. "Vector Space and Linear Maps." In Classical Mechanics with Mathematica®, 3–16. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-77595-1_1.

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Romano, Antonio. "Vector Space and Linear Maps." In Classical Mechanics with Mathematica®, 3–15. Boston, MA: Birkhäuser Boston, 2012. http://dx.doi.org/10.1007/978-0-8176-8352-8_1.

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Dalecky, Yu L., and S. V. Fomin. "Measures in linear topological spaces." In Measures and Differential Equations in Infinite-Dimensional Space, 83–107. Dordrecht: Springer Netherlands, 1991. http://dx.doi.org/10.1007/978-94-011-2600-7_4.

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Conference papers on the topic "Linear topological vector space"

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Bao, Yuanlu, Zhenan Liu, and Jin Qu. "An effective topological adjustment on vector maps for AVL." In International Conference on Space information Technology, edited by Cheng Wang, Shan Zhong, and Xiulin Hu. SPIE, 2005. http://dx.doi.org/10.1117/12.657414.

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Gu, Guomin, and Weihong Wang. "Improved Vector Route Algorithm Bases on Raster Topological Space Model." In TENCON 2005 - 2005 IEEE Region 10 Conference. IEEE, 2005. http://dx.doi.org/10.1109/tencon.2005.301072.

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Pucci, Marcello. "State space-vector model of linear induction motors." In 2012 IEEE Energy Conversion Congress and Exposition (ECCE). IEEE, 2012. http://dx.doi.org/10.1109/ecce.2012.6342390.

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"Non-linear Transformations of Vector Space Embedded Graphs." In 8th International Workshop on Pattern Recognition in Information Systems. SciTePress - Science and and Technology Publications, 2008. http://dx.doi.org/10.5220/0001744301730183.

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Kokubu, Masatoshi. "Linear Weingarten Surfaces in Hyperbolic Three-space." In INTERNATIONAL WORKSHOP ON COMPLEX STRUCTURES, INTEGRABILITY AND VECTOR FIELDS. AIP, 2011. http://dx.doi.org/10.1063/1.3567125.

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Mohamed, Essam E. M., Mahmoud A. Sayed, and Tarek Hassan Mohamed. "Sliding mode control of linear induction motors using space vector controlled inverter." In 2013 International Conference on Renewable Energy Research and Applications (ICRERA). IEEE, 2013. http://dx.doi.org/10.1109/icrera.2013.6749835.

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Boutet, P., J. Dubouloy, M. Soulard, and J. Pinho. "Fully Integrated QPSK Linear Vector Modulator for Space Applications in Ku Band." In 28th European Microwave Conference, 1998. IEEE, 1998. http://dx.doi.org/10.1109/euma.1998.338183.

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Baby, Renjith, C. Santhosh Kumar, Kuruvachan K. George, and Ashish Panda. "Noise compensation in i-vector space using linear regression for robust speaker verification." In 2017 International Conference on Multimedia, Signal Processing and Communication Technologies (IMPACT). IEEE, 2017. http://dx.doi.org/10.1109/mspct.2017.8363996.

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Pal, Krishan, and Mayank Sharma. "Performance evaluation of non-linear techniques UMAP and t-SNE for data in higher dimensional topological space." In 2020 Fourth International Conference on I-SMAC (IoT in Social, Mobile, Analytics and Cloud) (I-SMAC). IEEE, 2020. http://dx.doi.org/10.1109/i-smac49090.2020.9243502.

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Kou, Baoquan, Feng Xing, Chaoning Zhang, Lu Zhang, and Hao Yan. "Synchronous control of dual linear motors based on advanced space voltage vector switch table." In 2014 17th International Symposium on Electromagnetic Launch Technology (EML). IEEE, 2014. http://dx.doi.org/10.1109/eml.2014.6920673.

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Reports on the topic "Linear topological vector space"

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Frigo, Nicholas J., Vincent J. Urick, and Frank Bucholtz. Modeling Interferometric Structures with Birefringent Elements: A Linear Vector-Space Formalism. Fort Belvoir, VA: Defense Technical Information Center, November 2013. http://dx.doi.org/10.21236/ada594532.

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