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Journal articles on the topic 'Spectral theory (Mathematics)'

Author: Grafiati

Published: 4 June 2021

Last updated: 1 August 2024

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1

Laursen, K. B. "Essential spectra through local spectral theory." Proceedings of the American Mathematical Society 125, no. 5 (1997): 1425–34. http://dx.doi.org/10.1090/s0002-9939-97-03852-5.

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2

Garkusha, Grigory. "Correspondences and stable homotopy theory." Transactions of the London Mathematical Society 10, no. 1 (September 28, 2023): 124–55. http://dx.doi.org/10.1112/tlm3.12056.

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AbstractA general method of producing correspondences and spectral categories out of symmetric ring objects in general categories is given. As an application, stable homotopy theory of spectra is recovered from modules over a commutative symmetric ring spectrum defined in terms of framed correspondences over an algebraically closed field. Another application recovers stable motivic homotopy theory from spectral modules over associated spectral categories.

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3

Wong, M. W. "Weak spectral theory." Proceedings of the American Mathematical Society 95, no. 3 (March 1, 1985): 429. http://dx.doi.org/10.1090/s0002-9939-1985-0806082-9.

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4

Laursen, Kjeld B., and Michael M. Neumann. "Local spectral theory and spectral inclusions." Glasgow Mathematical Journal 36, no. 3 (September 1994): 331–43. http://dx.doi.org/10.1017/s0017089500030937.

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Suppose that T and S are continuous linear operators on complex Banach spaces X and Y, respectively, and that A is a non-zero continuous linear mapping from X to Y. If A intertwines T and S in the sense that SA = AT, then a classical result due to Rosenblum implies that the spectra σ(T) and σ(S) must overlap, see [12]. Actually, Davis and Rosenthal [5]have shown that the surjectivity spectrum σsu(T) will meet the approximate point spectrum σap(S) in this case (terms to be denned below). Further information about the relations between the two spectra and their finer structure becomes available when the intertwiner A is injective or has dense range, see [9], [12], [13].

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5

Vishik, M. M. "Nonarchimedean spectral theory." Journal of Soviet Mathematics 30, no. 6 (September 1985): 2513–55. http://dx.doi.org/10.1007/bf02249122.

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6

Putinar, Mihai. "Spectral theory and sheaf theory. II." Mathematische Zeitschrift 192, no. 3 (September 1986): 473–90. http://dx.doi.org/10.1007/bf01164022.

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7

Aiena, Pietro, and Maria Teresa Biondi. "Some spectral mapping theorems through local spectral theory." Rendiconti del Circolo Matematico di Palermo 53, no. 2 (June 2004): 165–84. http://dx.doi.org/10.1007/bf02872869.

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8

Hafner, James Lee. "Application of spectral theory to number theory." Rocky Mountain Journal of Mathematics 15, no. 2 (June 1985): 389–98. http://dx.doi.org/10.1216/rmj-1985-15-2-389.

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9

Carpintero, C., A. Gutierrez, E. Rosas, and J. Sanabria. "A note on preservation of generalized Fredholm spectra in Berkani’s sense." Filomat 32, no. 18 (2018): 6431–40. http://dx.doi.org/10.2298/fil1818431c.

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In this paper, we study the relationships between the spectra derived from B-Fredholm theory corresponding to two given bounded linear operators. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from B-Fredholm theory corresponding to two given operators are respectively the same. Among other results, we prove that B-Fredholm type spectral properties for an operator and its restriction are equivalent, as well as obtain conditions for which B-Fredholm type spectral properties corresponding to two given operators are the same. As application of our results, we obtain conditions for which the above mentioned spectra and the spectra derived from the classical Fredholm theory are the same.

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10

Sachs, Robert L. "Book Review: Inverse spectral theory." Bulletin of the American Mathematical Society 19, no. 1 (July 1, 1988): 362–67. http://dx.doi.org/10.1090/s0273-0979-1988-15676-5.

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11

Curto, Raúl E., and Keren Yan. "Spectral theory of Reinhardt measures." Bulletin of the American Mathematical Society 24, no. 2 (April 1, 1991): 379–86. http://dx.doi.org/10.1090/s0273-0979-1991-16040-4.

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12

León-Saavedra, Fernando, and Alfonso Montes-Rodríguez. "Spectral theory and hypercyclic subspaces." Transactions of the American Mathematical Society 353, no. 1 (September 13, 2000): 247–67. http://dx.doi.org/10.1090/s0002-9947-00-02743-4.

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13

CORNEA, O., K. A. DE REZENDE, and M. R. DA SILVEIRA. "Spectral sequences in Conley’s theory." Ergodic Theory and Dynamical Systems 30, no. 4 (October 13, 2009): 1009–54. http://dx.doi.org/10.1017/s0143385709000479.

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AbstractIn this paper, we analyse the dynamics encoded in the spectral sequence (Er,dr) associated with certain Conley theory connection maps in the presence of an ‘action’ type filtration. More specifically, we present an algorithm for finding a chain complex C and its differential; the method uses a connection matrix Δ to provide a system that spans Er in terms of the original basis of C and to identify all of the differentials drp:Erp→Erp−r. In exploring the dynamical implications of a non-zero differential, we prove the existence of a path that joins the singularities generating E0p and E0p−r in the case where a direct connection by a flow line does not exist. This path is made up of juxtaposed orbits of the flow and of the reverse flow, and proves to be important in some applications.

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14

Dutkay, Dorin Ervin, and Palle E. T. Jorgensen. "Spectral Theory for Discrete Laplacians." Complex Analysis and Operator Theory 4, no. 1 (April 14, 2009): 1–38. http://dx.doi.org/10.1007/s11785-008-0098-2.

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15

Langer, Heinz, Branko Najman, and Christiane Tretter. "Spectral Theory of the Klein–Gordon Equation in Krein Spaces." Proceedings of the Edinburgh Mathematical Society 51, no. 3 (October 2008): 711–50. http://dx.doi.org/10.1017/s0013091506000150.

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AbstractIn this paper the spectral properties of the abstract Klein–Gordon equation are studied. The main tool is an indefinite inner product known as the charge inner product. Under certain assumptions on the potential V, two operators are associated with the Klein–Gordon equation and studied in Krein spaces generated by the charge inner product. It is shown that the operators are self-adjoint and definitizable in these Krein spaces. As a consequence, they possess spectral functions with singularities, their essential spectra are real with a gap around 0 and their non-real spectra consist of finitely many eigenvalues of finite algebraic multiplicity which are symmetric to the real axis. One of these operators generates a strongly continuous group of unitary operators in the Krein space; the other one gives rise to two bounded semi-groups. Finally, the results are applied to the Klein–Gordon equation in ℝn.

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16

Davies, E. B. "ALGEBRAIC ASPECTS OF SPECTRAL THEORY." Mathematika 57, no. 1 (December 21, 2010): 63–88. http://dx.doi.org/10.1112/s0025579310001579.

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17

Pearson, D. B. "Value Distribution and Spectral Theory." Proceedings of the London Mathematical Society s3-68, no. 1 (January 1994): 127–44. http://dx.doi.org/10.1112/plms/s3-68.1.127.

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18

Girko, V. L. "Spectral theory of random matrices." Russian Mathematical Surveys 40, no. 1 (February 28, 1985): 77–120. http://dx.doi.org/10.1070/rm1985v040n01abeh003528.

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19

Rota, Gian-Carlo. "Pseudodifferential operators and spectral theory." Advances in Mathematics 68, no. 1 (March 1988): 85. http://dx.doi.org/10.1016/0001-8708(88)90010-2.

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20

Tabuada, Gonçalo. "Homotopy theory of spectral categories." Advances in Mathematics 221, no. 4 (July 2009): 1122–43. http://dx.doi.org/10.1016/j.aim.2009.01.014.

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21

Breuer, Jonathan, and Barry Simon. "Natural boundaries and spectral theory." Advances in Mathematics 226, no. 6 (April 2011): 4902–20. http://dx.doi.org/10.1016/j.aim.2010.12.019.

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22

Coons, Michael, James Evans, and Neil Mañibo. "Spectral theory of regular sequences." Documenta Mathematica 27 (2022): 629–53. http://dx.doi.org/10.4171/dm/880.

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23

Kats, I. S. "Spectral theory of a string." Ukrainian Mathematical Journal 46, no. 3 (March 1994): 159–82. http://dx.doi.org/10.1007/bf01062233.

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24

Girko, Vyacheslav L. "Spectral theory of minimax estimation." Acta Applicandae Mathematicae 43, no. 1 (April 1996): 59–69. http://dx.doi.org/10.1007/bf00046987.

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25

Livernet, Muriel, and Sarah Whitehouse. "Homotopy theory of spectral sequences." Homology, Homotopy and Applications 26, no. 1 (2024): 69–86. http://dx.doi.org/10.4310/hha.2024.v26.n1.a5.

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26

HOVEY, MARK. "THE GENERALIZED HOMOLOGY OF PRODUCTS." Glasgow Mathematical Journal 49, no. 1 (January 2007): 1–10. http://dx.doi.org/10.1017/s0017089507003369.

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Abstract.We construct a spectral sequence that computes the generalized homology E*(∏ Xα) of a product of spectra. The E2-term of this spectral sequence consists of the right derived functors of product in the category of E*E-comodules, and the spectral sequence always converges when E is the Johnson-Wilson theory E(n) and the Xα are Ln-local. We are able to prove some results about the E2-term of this spectral sequence; in particular, we show that the E(n)-homology of a product of E(n)-module spectra Xα is just the comodule product of the E(n)*Xα. This spectral sequence is relevant to the chromatic splitting conjecture.

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27

Djordjević, S. V., and H. Zguitti. "Essential point spectra of operator matrices trough local spectral theory." Journal of Mathematical Analysis and Applications 338, no. 1 (February 2008): 285–91. http://dx.doi.org/10.1016/j.jmaa.2007.05.031.

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28

Zerouali, El Hassan, and Hassane Zguitti. "Perturbation of spectra of operator matrices and local spectral theory." Journal of Mathematical Analysis and Applications 324, no. 2 (December 2006): 992–1005. http://dx.doi.org/10.1016/j.jmaa.2005.12.065.

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29

Arendtsz, N. V., and E. M. A. Hussein. "Energy-spectral Compton scatter imaging. I. Theory and mathematics." IEEE Transactions on Nuclear Science 42, no. 6 (1995): 2155–65. http://dx.doi.org/10.1109/23.489441.

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30

Lisica, Ju T. "Theory of spectral sequences. II." Journal of Mathematical Sciences 146, no. 1 (October 2007): 5530–51. http://dx.doi.org/10.1007/s10958-007-0367-z.

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31

Petrov, A. M. "Spectral theory of bounded operators." Journal of Soviet Mathematics 49, no. 6 (May 1990): 1291–94. http://dx.doi.org/10.1007/bf02209175.

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32

Benzinger, Harold E. "Nonharmonic Fourier series and spectral theory." Transactions of the American Mathematical Society 299, no. 1 (January 1, 1987): 245. http://dx.doi.org/10.1090/s0002-9947-1987-0869410-0.

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33

Grunenfelder, Luzius, and Tomaž Košir. "Geometric aspects of multiparameter spectral theory." Transactions of the American Mathematical Society 350, no. 6 (1998): 2525–46. http://dx.doi.org/10.1090/s0002-9947-98-02078-9.

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34

Chagouel, Isaak, Michael Stessin, and Kehe Zhu. "Geometric spectral theory for compact operators." Transactions of the American Mathematical Society 368, no. 3 (June 15, 2015): 1559–82. http://dx.doi.org/10.1090/tran/6588.

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35

Baudel, Manon, and Nils Berglund. "Spectral Theory for Random Poincaré Maps." SIAM Journal on Mathematical Analysis 49, no. 6 (January 2017): 4319–75. http://dx.doi.org/10.1137/16m1103816.

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36

Faierman, Melvin. "The Interior Transmission Problem: Spectral Theory." SIAM Journal on Mathematical Analysis 46, no. 1 (January 2014): 803–19. http://dx.doi.org/10.1137/130922215.

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37

Weiddman, J. "SPECTRAL THEORY AND DIFFERENTIAL OPERATORS (Oxford Mathematical Monographs)." Bulletin of the London Mathematical Society 21, no. 4 (July 1989): 407–9. http://dx.doi.org/10.1112/blms/21.4.407.

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38

Kirkland, Stephen, and Norman J. Pullman. "Boolean spectral theory." Linear Algebra and its Applications 175 (October 1992): 177–90. http://dx.doi.org/10.1016/0024-3795(92)90308-w.

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39

Arsic, Branko, Dragos Cvetkovic, Slobodan Simic, and Milan Skaric. "Graph spectral techniques in computer sciences." Applicable Analysis and Discrete Mathematics 6, no. 1 (2012): 1–30. http://dx.doi.org/10.2298/aadm111223025a.

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We give a survey of graph spectral techniques used in computer sciences. The survey consists of a description of particular topics from the theory of graph spectra independently of the areas of Computer science in which they are used. We have described the applications of some important graph eigenvalues (spectral radius, algebraic connectivity, the least eigenvalue etc.), eigenvectors (principal eigenvector, Fiedler eigenvector and other), spectral reconstruction problems, spectra of random graphs, Hoffman polynomial, integral graphs etc. However, for each described spectral technique we indicate the fields in which it is used (e.g. in modelling and searching Internet, in computer vision, pattern recognition, data mining, multiprocessor systems, statistical databases, and in several other areas). We present some novel mathematical results (related to clustering and the Hoffman polynomial) as well.

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40

Boua, Hamid, Mohammed Karmouni, and Abdelaziz Tajmouati. "$C_0$-semigroups and Local spectral theory." Boletim da Sociedade Paranaense de Matemática 40 (February 7, 2022): 1–5. http://dx.doi.org/10.5269/bspm.52765.

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Let $(T(t))_{t\geq0}$ be a $C_{0}$-semigroup of operators on a Banach space $X$. In this paper, we show that if there exists $t_0>0$ such that $T(t_0)$ has the SVEP then $(T(t))_{t\geq0}$ has the SVEP. Also, some local spectral properties for $C_0$ semigroups and theirs generators and some stabilities results are also established.

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41

Douglas, Ronald G., and Jerome Kaminker. "Spectral Multiplicity and Odd K-theory." Pure and Applied Mathematics Quarterly 6, no. 2 (2010): 307–30. http://dx.doi.org/10.4310/pamq.2010.v6.n2.a2.

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42

Donnelly, Harold. "Spectral Theory of Complete Riemannian Manifolds." Pure and Applied Mathematics Quarterly 6, no. 2 (2010): 439–56. http://dx.doi.org/10.4310/pamq.2010.v6.n2.a7.

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43

Brahim, Fatma, Aref Jeribi, and Bilel Krichen. "Spectral theory for polynomially demicompact operators." Filomat 33, no. 7 (2019): 2017–30. http://dx.doi.org/10.2298/fil1907017b.

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In this article, we introduce the notion of polynomial demicompactness and we use it to give some results on Fredholm operators and to establish a fine description of some essential spectra of a closed densely defined linear operator. Our work is a generalization of many known ones in the literature.

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44

Elbjaoui, H., and E. H. Zerouali. "Local spectral theory for2×2operator matrices." International Journal of Mathematics and Mathematical Sciences 2003, no. 42 (2003): 2667–72. http://dx.doi.org/10.1155/s0161171203012043.

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We discuss the spectral properties of the operatorMC∈ℒ(X⊕Y)defined byMC:=(AC0B), whereA∈ℒ(X),B∈ℒ(Y),C∈ℒ(Y,X), andX,Yare complex Banach spaces. We prove that(SA∗∩SB)∪σ(MC)=σ(A)∪σ(B)for allC∈ℒ(Y,X). This allows us to give a partial positive answer to Question 3 of Du and Jin (1994) and generalizations of some results of Houimdi and Zguitti (2000). Some applications to the similarity problem are also given.

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45

LIU, XIAOGANG. "SELECTED TOPICS IN SPECTRAL GRAPH THEORY." Bulletin of the Australian Mathematical Society 93, no. 3 (February 17, 2016): 511–12. http://dx.doi.org/10.1017/s0004972715001768.

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46

Millionshchikov, D. V. "Spectral sequences in analytic homotopy theory." Mathematical Notes of the Academy of Sciences of the USSR 47, no. 5 (May 1990): 458–64. http://dx.doi.org/10.1007/bf01158088.

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47

Rota, Gian-Carlo. "Spectral methods in linear transport theory." Advances in Mathematics 58, no. 3 (December 1985): 322. http://dx.doi.org/10.1016/0001-8708(85)90123-9.

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48

Swaters, Gordon E. "Spectral Properties in Modon Stability Theory." Studies in Applied Mathematics 112, no. 3 (April 2004): 235–58. http://dx.doi.org/10.1111/j.0022-2526.2004.01506.x.

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49

Montes-Rodríguez, Alfonso, Alejandro Rodríguez-Martínez, and Stanislav Shkarin. "Spectral theory of Volterra-composition operators." Mathematische Zeitschrift 261, no. 2 (May 9, 2008): 431–72. http://dx.doi.org/10.1007/s00209-008-0365-y.

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50

Wong, M. W. "Spectral Theory of Pseudo-Differential Operators." Advances in Applied Mathematics 15, no. 4 (December 1994): 437–51. http://dx.doi.org/10.1006/aama.1994.1018.

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