Relevant bibliographies by topics / Inner product spaces and their generalizations

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Inner product spaces and their generalizations'

Author: Grafiati
Published: 4 June 2021
Last updated: 5 February 2022

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Journal articles on the topic "Inner product spaces and their generalizations"

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Jayaraman, Sachindranath. "Nonnegative generalized inverses in indefinite inner product spaces." Filomat 27, no. 4 (2013): 659–70. http://dx.doi.org/10.2298/fil1304659j.

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The aim of this article is to investigate nonnegativity of the inverse, the Moore-Penrose inverse and other generalized inverses, in the setting of indefinite inner product spaces with respect to the indefinite matrix product. We also propose and investigate generalizations of the corresponding notions of matrix monotonicity, namely, o-(rectangular) monotonicity, o-semimonotonicity and ?-weak monotonicity and its interplay with nonnegativity of various generalized inverses in the same setting.
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Ebanks, B. R., PL Kannappan, and P. K. Sahoo. "A Common Generalization of Functional Equations Characterizing Normed and Quasi-Inner-Product Spaces." Canadian Mathematical Bulletin 35, no. 3 (September 1, 1992): 321–27. http://dx.doi.org/10.4153/cmb-1992-044-6.

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AbstractWe determine the general solutions of the functional equation for ƒi: G → F (i = 1,2,3,4), where G is a 2-divisible group and F is a commutative field of characteristic different from 2. The motivation for studying this equation came from a result due to Dry gas [4] where he proved a Jordan and von Neumann type characterization theorem for quasi-inner products. Also, this equation is a generalization of the quadratic functional equation investigated by several authors in connection with inner product spaces and their generalizations. Special cases of this equation include the Cauchy equation, the Jensen equation, the Pexider equation and many more. Here, we determine the general solution of this equation without any regularity assumptions on ƒi.
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Ceno, Stela. "Some properties of the superior and inferior semi inner product function associated to the 2-norm." JOURNAL OF ADVANCES IN MATHEMATICS 12, no. 5 (June 30, 2016): 6254–60. http://dx.doi.org/10.24297/jam.v12i5.322.

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Special properties that the scalar product enjoys and its close link with the norm function have raised the interest of researchers from a very long period of time. S.S. Dragomir presents concrete generalizations of the scalar product functions in a normed space and deals with the interesting properties of them. Based on S.S. Dragomirs idea in this paper we treat generalizations of superior and inferior scalar product functions in the case of semi-normed spaces and 2-normed spaces.
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Kechriniotis, AristidesI, and KonstantinosK Delibasis. "On Generalizations of Grüss Inequality in Inner Product Spaces and Applications." Journal of Inequalities and Applications 2010, no. 1 (2010): 167091. http://dx.doi.org/10.1155/2010/167091.

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Alomari, Mohammad W. "On Pompeiu Cebysev Type Inequalities for Positive Linear Maps of Selfadjoint Operators in Inner Product Spaces." JOURNAL OF ADVANCES IN MATHEMATICS 15 (December 1, 2018): 8081–92. http://dx.doi.org/10.24297/jam.v15i0.7927.

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In this work, generalizations of some inequalities for continuous synchronous (h-asynchronous) functions of linear bounded selfadjoint operators under positive linear maps in Hilbert spaces are proved.
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Pecaric, J. "On Hua's inequality in real inner product spaces." Tamkang Journal of Mathematics 33, no. 3 (September 30, 2002): 265–68. http://dx.doi.org/10.5556/j.tkjm.33.2002.265-268.

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DRAGOMIR, S. S., and G. S. YANG. "ON HUA'S INEQUALITY IN REAL INNER PRODUCT SPACES." Tamkang Journal of Mathematics 27, no. 3 (September 1, 1997): 227–32. http://dx.doi.org/10.5556/j.tkjm.27.1996.4338.

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RADAS, SONJA, and TOMISLAV SIKIC. "A NOTE ON THE GENERALIZATION OF HUA'S INEQUALITY." Tamkang Journal of Mathematics 28, no. 4 (December 1, 1997): 321–23. http://dx.doi.org/10.5556/j.tkjm.28.1997.4310.

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In this paper we establish Lo-Keng Hua's inequality for linear operators in real inner product spaces. Our result generalizes Hua's inequality in real inner product spaces, obtained recently by S. S. Dragomir and G.-S. Yang.
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Malejki, Renata. "Stability of a generalization of the Fréchet functional equation." Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica 14, no. 1 (December 1, 2015): 69–79. http://dx.doi.org/10.1515/aupcsm-2015-0006.

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AbstractWe prove some stability and hyperstability results for a generalization of the well known Fréchet functional equation, stemming from one of the characterizations of the inner product spaces. As the main tool we use a fixed point theorem for some function spaces. We end the paper with some new inequalities characterizing the inner product spaces.
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Dragomir, S. S. "Generalizations of Buzano inequality for $n$-tuples of vectors in inner product spaces with applications." Tbilisi Mathematical Journal 10, no. 2 (February 2017): 29–42. http://dx.doi.org/10.1515/tmj-2017-0023.

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Dissertations / Theses on the topic "Inner product spaces and their generalizations"

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Wigren, Thomas. "The Cauchy-Schwarz inequality : Proofs and applications in various spaces." Thesis, Karlstads universitet, Avdelningen för matematik, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-38196.

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We give some background information about the Cauchy-Schwarz inequality including its history. We then continue by providing a number of proofs for the inequality in its classical form using various proof techniques, including proofs without words. Next we build up the theory of inner product spaces from metric and normed spaces and show applications of the Cauchy-Schwarz inequality in each content, including the triangle inequality, Minkowski's inequality and Hölder's inequality. In the final part we present a few problems with solutions, some proved by the author and some by others.
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Wu, Senlin. "Geometry of Minkowski Planes and Spaces -- Selected Topics." Doctoral thesis, [S.l. : s.n.], 2009. http://nbn-resolving.de/urn:nbn:de:bsz:ch1-200900226.

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Moldenhauer, Anja I. S. [Verfasser], and Gerhard [Akademischer Betreuer] Rosenberger. "Cryptographic protocols based on inner product spaces and group theory with a special focus on the use of Nielsen transformations / Anja I. S. Moldenhauer ; Betreuer: Gerhard Rosenberger." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2016. http://d-nb.info/1120623340/34.

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Moldenhauer, Anja I. S. Verfasser], and Gerhard [Akademischer Betreuer] [Rosenberger. "Cryptographic protocols based on inner product spaces and group theory with a special focus on the use of Nielsen transformations / Anja I. S. Moldenhauer ; Betreuer: Gerhard Rosenberger." Hamburg : Staats- und Universitätsbibliothek Hamburg, 2016. http://nbn-resolving.de/urn:nbn:de:gbv:18-82092.

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Góis, Aédson Nascimento. "Elementos da análise funcional para o estudo da equação da corda vibrante." Universidade Federal de Sergipe, 2016. https://ri.ufs.br/handle/riufs/6511.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
In this work, we are treated some elements of functional analysis such as Banach spaces, inner product spaces and Hilbert spaces, also studied Fourier series and at the end briefly consider the equation of the vibrating string. With this, you realize that you do not need a lot of theory in order to get significant results.
Neste trabalho, são tratados alguns elementos da análise funcional como espaços de Banach, espaços com produto interno e espaços de Hilbert, estudamos também séries de Fourier e no final consideramos brevemente a equação da corda vibrante. Com isso, percebe-se que não se precisa de muita teoria para conseguirmos resultados significativos.
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Gowda, Huche. "Studies in semi-inner product spaces." Thesis, 1987. http://hdl.handle.net/2009/1426.

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Jasinski, Jakub. "Hrushovski and Ramsey Properties of Classes of Finite Inner Product Structures, Finite Euclidean Metric Spaces, and Boron Trees." Thesis, 2011. http://hdl.handle.net/1807/29762.

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We investigate two combinatorial properties of classes of finite structures, as well as related applications to topological dynamics. Using the Hrushovski property of classes of finite structures -- a finite extension property of homomorphisms -- we can show the existence of ample generics. For example, Solecki proved the existence of ample generics in the context of finite metric spaces that do indeed possess this extension property. Furthermore, Kechris, Pestov and Todorcevic have shown that the Ramsey property of Fraisse classes of finite structures implies that the automorphism group of the corresponding Fraisse limit is extremely amenable, i.e., it possesses a very strong fixed point property. Gromov and Milman had shown that the unitary group of the infinite-dimensional separable Hilbert space is extremely amenable using non-combinatorial methods. This result encourages a deeper look into structural Euclidean Ramsey theory, i.e., Euclidean Ramsey theory in which we colour more than just points. In particular, we look at complete finite labeled graphs whose vertex sets are subsets of the Hilbert space and whose labels correspond to the inner products. We prove "Ramsey-type" and "Hrushovski-type" theorems for linearly ordered metric subspaces of "sufficiently" orthogonal sets. In particular, the latter is used to show a "Hrushovski version" of the Ramsey-type Matousek-Rodl theorem for simplices. It is known that the square root of the metric induced by the distance between vertices in graphs produces a metric space embeddable in a Euclidean space if and only if the graph is a metric subgraph of the Cartesian product of three types of graphs. These three are the half-cube graphs, the so-called cocktail party graphs, and the Gosset graph. We show that the class of metric spaces related to half-cube graphs -- metric spaces on sets with the symmetric difference metric -- satisfies the Hrushovski property up to 3 points, but not more. Moreover, the amalgamation in this class can be too restrictive to permit the Ramsey Property. Finally, following the work of Fouche, we compute the Ramsey degrees of structures induced by the leaf sets of boron trees. Also, we briefly show that this class does not satisfy the full Hrushovski property. Fouche's trees are in fact related to ultrametric spaces, as was observed by Lionel Nguyen van The. We augment Fouche's concept of orientation so that it applies to these boron tree structures. The upper bound computation of the Ramsey degree in this case, turns out to be an "asymmetric" version of the Graham-Rothschild theorem. Finally, we extend these structures to "oriented" ones, yielding a Ramsey class and a corresponding Fraisse limit whose automorphism group is extremely amenable.
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Van, Rensburg Dawid Benjamin Janse. "Structures matrices in indefinite inner product spaces : simple forms, invariant subspaces and rank-one perturbations / Dawid Benjamin Janse van Rensburg." Thesis, 2012. http://hdl.handle.net/10394/11057.

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The (definite) inner product between P two vectors x; y 2 Rn is defined by (x,y) = [not able to show]. The length of a vector x 2 Rn is then described by the inner product as [not able to show]. In this thesis the definite inner product is replaced by an indefinite inner product. This has a substantial impact on the geometry of subspaces. The indefinite inner product between two vectors in Rn can uniquely be represented by [x; y] = hHx; yi, for a real invertible symmetric matrix H = HT . In the literature there exists an extensive theory for the classes of hermitian, unitary and normal matrices for the definite inner product space. Similar classes are also studied in the context of indefinite inner product space. In this thesis we focus on a study of H-positive real and H-expansive matrices. This study is closely related to a thorough study of H-dissipative and H-contractive matrices, which already exists in the literature. In Chapter 2 we discuss a class of matrices that is closely related to H-dissipative matrices, namely, the class of H-positive real matrices. A matrix A is H-dissipative if [not able to show]. A non-complex matrix A is H-positive real if [not able to show]. It is easily seen that A is H-positive real if and only if iA is H-dissipative, and hence it follows that -iA is H-positive real if and only if A is H-dissipative. A simple form for the matrix H is obtained and thereafter the A-invariant maximal H-nonnegative and H-non-positive subspaces are constructed. The main focus however, is to obtain the uniqueness and stability of these subspaces. The numerical range condition is used for this purpose. Both the real and complex cases are treated in this chapter. In Chapter 3 a second class of matrices in the indefinite inner product space is considered, namely the class of H-expansive matrices. These are matrices A for which A_HA*H is nonnegative. As in the previous chapter, our purpose is the construction of complex (as well as real) A-invariant maximal H-nonnegative and A-invariant maximal H-non-positive subspaces. Alternatively, we could have used a suitable Cayley transform to obtain the same results, except for the case when A is real and has both the eigenvalues 1 and -1. The techniques developed in this thesis covers this case. The techniques again entail that a simple form for the matrix pair (A,H) is obtained, with A in Jordan canonical form or in the real canonical form. The simple form is then used to construct the A-invariant maximal H-nonnegative and A-invariant maximal H-non-positive subspaces. The last section of the chapter is devoted to obtaining a simple form for the class of H-unitary matrices. We say a real matrix A is H-unitary if ATHA-H = 0, for any real symmetric invertible matrix H. What complicates matters here are if A has eigenvalues +-1 and the corresponding Jordan blocks are of even size. In the final chapter of the thesis a different topic is considered, namely, rank-one perturbations of H-positive real matrices. A rank-one perturbation of a matrix A is given by B = A + uv*, where u and v are in Cn. We mainly consider perturbations that have the additional structure that uv* is itself H-positive real. We are interested in the generic behaviour of eigenvalues under such structured rank-one perturbations. A new and interesting result is obtained; that eigenvalues introduced by the perturbation cannot lie on the imaginary axis. However, asymptotically, they may tend towards the imaginary axis. The chapter ends with a few examples which illustrate an interesting phenomenon which occurs when considering rank-one perturbations in the real case.
Thesis (PhD (Mathematics))--North-West University, Potchefstroom Campus, 2012
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Wu, Senlin. "Geometry of Minkowski Planes and Spaces -- Selected Topics." Doctoral thesis, 2008. https://monarch.qucosa.de/id/qucosa%3A19070.

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The results presented in this dissertation refer to the geometry of Minkowski spaces, i.e., of real finite-dimensional Banach spaces. First we study geometric properties of radial projections of bisectors in Minkowski spaces, especially the relation between the geometric structure of radial projections and Birkhoff orthogonality. As an application of our results it is shown that for any Minkowski space there exists a number, which plays somehow the role that $\sqrt2$ plays in Euclidean space. This number is referred to as the critical number of any Minkowski space. Lower and upper bounds on the critical number are given, and the cases when these bounds are attained are characterized. Moreover, with the help of the properties of bisectors we show that a linear map from a normed linear space $X$ to another normed linear space $Y$ preserves isosceles orthogonality if and only if it is a scalar multiple of a linear isometry. Further on, we examine the two tangent segments from any exterior point to the unit circle, the relation between the length of a chord of the unit circle and the length of the arc corresponding to it, the distances from the normalization of the sum of two unit vectors to those two vectors, and the extension of the notions of orthocentric systems and orthocenters in Euclidean plane into Minkowski spaces. Also we prove theorems referring to chords of Minkowski circles and balls which are either concurrent or parallel. All these discussions yield many interesting characterizations of the Euclidean spaces among all (strictly convex) Minkowski spaces. In the final chapter we investigate the relation between the length of a closed curve and the length of its midpoint curve as well as the length of its image under the so-called halving pair transformation. We show that the image curve under the halving pair transformation is convex provided the original curve is convex. Moreover, we obtain several inequalities to show the relation between the halving distance and other quantities well known in convex geometry. It is known that the lower bound for the geometric dilation of rectifiable simple closed curves in the Euclidean plane is $\pi/2$, which can be attained only by circles. We extend this result to Minkowski planes by proving that the lower bound for the geometric dilation of rectifiable simple closed curves in a Minkowski plane $X$ is analogously a quarter of the circumference of the unit circle $S_X$ of $X$, but can also be attained by curves that are not Minkowskian circles. In addition we show that the lower bound is attained only by Minkowskian circles if the respective norm is strictly convex. Also we give a sufficient condition for the geometric dilation of a closed convex curve to be larger than a quarter of the perimeter of the unit circle.
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Books on the topic "Inner product spaces and their generalizations"

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Antoine, Jean-Pierre, and Camillo Trapani. Partial Inner Product Spaces. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-05136-4.

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Amir, Dan. Characterizations of inner product spaces. Basel: Birkhäuser Verlag, 1986.

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Amir, Dan. Characterizations of Inner Product Spaces. Basel: Birkhäuser Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-5487-0.

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Functional analysis: An elementary introduction. Providence, Rhode Island: American Mathematical Society, 2014.

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Deutsch, Frank. Best Approximation in Inner Product Spaces. New York, NY: Springer New York, 2001. http://dx.doi.org/10.1007/978-1-4684-9298-9.

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Förster, Karl-Heinz, Peter Jonas, Heinz Langer, and Carsten Trunk, eds. Operator Theory in Inner Product Spaces. Basel: Birkhäuser Basel, 2007. http://dx.doi.org/10.1007/978-3-7643-8270-4.

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Deutsch, Frank. Best Approximation in Inner Product Spaces. New York, NY: Springer New York, 2001.

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(Camillo), Trapani C., ed. Partial inner product spaces: Theory and applications. Heidelberg: Springer-Verlag, 2009.

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Langer, Matthias, Annemarie Luger, and Harald Woracek, eds. Operator Theory and Indefinite Inner Product Spaces. Basel: Birkhäuser Basel, 2006. http://dx.doi.org/10.1007/3-7643-7516-7.

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Alsina, Claudi. Norm derivatives and characterizations of inner product spaces. Singapore: World Scientific, 2010.

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Book chapters on the topic "Inner product spaces and their generalizations"

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Berschneider, Georg, and Zoltán Sasvári. "Spectral Theory of Stationary Random Fields and their Generalizations. A Short Historical Survey." In Indefinite Inner Product Spaces, Schur Analysis, and Differential Equations, 217–35. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-68849-7_8.

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Beilina, Larisa, Evgenii Karchevskii, and Mikhail Karchevskii. "Inner Product Spaces." In Numerical Linear Algebra: Theory and Applications, 69–92. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57304-5_3.

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Axler, Sheldon. "Inner-Product Spaces." In Undergraduate Texts in Mathematics, 97–125. New York, NY: Springer New York, 1997. http://dx.doi.org/10.1007/0-387-22595-1_6.

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Knapp, Anthony W. "Inner-Product Spaces." In Basic Algebra, 89–116. Boston, MA: Birkhäuser Boston, 2006. http://dx.doi.org/10.1007/978-0-8176-4529-8_3.

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Valenza, Robert J. "Inner Product Spaces." In Linear Algebra, 131–50. New York, NY: Springer New York, 1993. http://dx.doi.org/10.1007/978-1-4612-0901-0_7.

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Petersen, Peter. "Inner Product Spaces." In Linear Algebra, 227–91. New York, NY: Springer New York, 2012. http://dx.doi.org/10.1007/978-1-4614-3612-6_3.

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Katznelson, Yitzhak, and Yonatan Katznelson. "Inner-product spaces." In The Student Mathematical Library, 103–34. Providence, Rhode Island: American Mathematical Society, 2007. http://dx.doi.org/10.1090/stml/044/06.

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Shi, Zhiping, Yong Guan, and Ximeng Li. "Inner-Product Spaces." In Formalization of Complex Analysis and Matrix Theory, 135–50. Singapore: Springer Singapore, 2020. http://dx.doi.org/10.1007/978-981-15-7261-6_9.

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Römisch, Werner, and Thomas Zeugmann. "Inner Product Spaces." In Mathematical Analysis and the Mathematics of Computation, 429–46. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-42755-3_9.

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Kwak, Jin Ho, and Sungpyo Hong. "Inner Product Spaces." In Linear Algebra, 157–99. Boston, MA: Birkhäuser Boston, 2004. http://dx.doi.org/10.1007/978-0-8176-8194-4_5.

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Conference papers on the topic "Inner product spaces and their generalizations"

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Hadi, Abdul, Mashadi, and Sri Gemawati. "On fuzzy n-inner product spaces." In INTERNATIONAL CONFERENCE AND WORKSHOP ON MATHEMATICAL ANALYSIS AND ITS APPLICATIONS (ICWOMAA 2017). Author(s), 2017. http://dx.doi.org/10.1063/1.5016644.

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Cole, Richard, José R. Correa, Vasilis Gkatzelis, Vahab Mirrokni, and Neil Olver. "Inner product spaces for MinSum coordination mechanisms." In the 43rd annual ACM symposium. New York, New York, USA: ACM Press, 2011. http://dx.doi.org/10.1145/1993636.1993708.

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Vijayakumar, S., and B. Baskaran. "A characterization of 2-inner product spaces." In 4TH INTERNATIONAL CONFERENCE ON THE SCIENCE AND ENGINEERING OF MATERIALS: ICoSEM2019. AIP Publishing, 2020. http://dx.doi.org/10.1063/5.0028293.

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Noriega, R., S. Abreo, and A. Ramirez. "Improving 2D FWI Performance By Using Symmetry On Inner Product Spaces." In First EAGE Workshop on High Performance Computing for Upstream in Latin America. Netherlands: EAGE Publications BV, 2018. http://dx.doi.org/10.3997/2214-4609.201803074.

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Bachrach, Yoram, Yehuda Finkelstein, Ran Gilad-Bachrach, Liran Katzir, Noam Koenigstein, Nir Nice, and Ulrich Paquet. "Speeding up the Xbox recommender system using a euclidean transformation for inner-product spaces." In the 8th ACM Conference. New York, New York, USA: ACM Press, 2014. http://dx.doi.org/10.1145/2645710.2645741.

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Jakubowski, Jacek, and Andrzej Michalski. "Estimation of Flow Parameters for the Needs of the Electromagnetic Measurement in Open Channels Based on a Concept of Inner Product Spaces." In 2007 IEEE Instrumentation & Measurement Technology Conference IMTC 2007. IEEE, 2007. http://dx.doi.org/10.1109/imtc.2007.379229.

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