Abstract:
A multidimensional analog of an asymptotic formula of G. Szegö for determinants of Toeplitz matrices is studied, and a continuous analog of the result is constructed.
Bibliography: 10 titles.
\Bibitem{Lin75}
\by I.~Yu.~Linnik
\paper A multidimensional analog of a~limit theorem of G.~Szeg\"o
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 6
\pages 1323--1332
\mathnet{http://mi.mathnet.ru/eng/im2097}
\crossref{https://doi.org/10.1070/IM1975v009n06ABEH001523}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=422974}
\zmath{https://zbmath.org/?q=an:0329.41022}
Linking options:
https://www.mathnet.ru/eng/im2097
https://doi.org/10.1070/IM1975v009n06ABEH001523
https://www.mathnet.ru/eng/im/v39/i6/p1393
This publication is cited in the following 12 articles:
Alexander V. Sobolev, Spectral Theory, Function Spaces and Inequalities, 2012, 211
A. V. Sobolev, “Quasi-Classical Asymptotics for Pseudodifferential Operators with Discontinuous Symbols: Widom's Conjecture”, Funct. Anal. Appl., 44:4 (2010), 313–317
R. Unanyan, M. Fleischhauer, “Entanglement and Criticality in Translationally Invariant Harmonic Lattice Systems with Finite-Range Interactions”, Phys Rev Letters, 95:26 (2005), 260604
I. B. Simonenko, “Szegő-Type Limit Theorems for Generalized Discrete Convolution Operators”, Math. Notes, 78:2 (2005), 239–250
I. B. Simonenko, “Szegö Type Limit Theorems for Multidimensional Discrete Convolution Operators with Continuous Symbols”, Funct. Anal. Appl., 35:1 (2001), 77–78
Richard Carey, Joel Pincus, “Perturbation vectors”, Integr equ oper theory, 35:3 (1999), 271
V. Guillemin, K. Okikiolu, “Spectral Asymptotics of Toeplitz Operators on Zoll Manifolds”, Journal of Functional Analysis, 146:2 (1997), 496
A. Böttcher, H. Widom, “Two Remarks on Spectral Approximations for Wiener-Hopf Operators”, J. Integral Equations Applications, 6:1 (1994)
A Seghier, “Inversion de la matrice de Toeplitz en d dimensions et développement asymptotique de la trace de l'inverse à l'ordre d”, Journal of Functional Analysis, 67:3 (1986), 380
R. Ya. Doktorskii, “G. Szegö's limit theorem in the multidimensional case”, Funct. Anal. Appl., 18:1 (1984), 61–62
V. S. Vladimirov, I. V. Volovich, “A statistical physics model”, Theoret. and Math. Phys., 54:1 (1983), 1–12
Harold Widom, “Szegö's limit theorem: The higher-dimensional matrix case”, Journal of Functional Analysis, 39:2 (1980), 182
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