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Funktsional. Anal. i Prilozhen., 2004, Volume 38, Issue 1, Pages 81–82 (Mi faa98)  

This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

Asymptotic Invertibility and the Collective Asymptotic Spectral Behavior of Generalized One-Dimensional Discrete Convolutions

O. N. Zabroda, I. B. Simonenko

Rostov State University, Faculty of Mechanics and Mathematics

Abstract: We study the asymptotic invertibility as $n\to+\infty$ of matrices of the form $\alpha_{kj}^{(n)}=a(k/n,j/n,k-j)$ and $\beta_{kj}^{(n)}=b(k/E(n),j/E(n),k-j)$, where $a$ and $b$ are functions defined on the sets $[0,1]\times[0,1]\times\mathbb{Z}$ and $[0,+\infty)\times[0,+\infty)\times\mathbb{Z}$, respectively, $E(n)\to+\infty$, and $n/E(n)\to+\infty$. The joint asymptotic behavior of the spectrum of these matrices is analyzed.

Keywords: asymptotic invertibility, matrix, operator, spectrum

DOI: https://doi.org/10.4213/faa98

Full text: PDF file (127 kB)
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English version:
Functional Analysis and Its Applications, 2004, 38:1, 65–66

Bibliographic databases:

UDC: 517.9
Received: 01.11.2002

Citation: O. N. Zabroda, I. B. Simonenko, “Asymptotic Invertibility and the Collective Asymptotic Spectral Behavior of Generalized One-Dimensional Discrete Convolutions”, Funktsional. Anal. i Prilozhen., 38:1 (2004), 81–82; Funct. Anal. Appl., 38:1 (2004), 65–66

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Bottcher, A, “Uniform boundedness of Toeplitz matrices with variable coefficients”, Integral Equations and Operator Theory, 60:3 (2008), 313  crossref  mathscinet  zmath  isi  scopus
    2. Mascarenhas H., Silbermann B., “Sequences of Variable-Coefficient Toeplitz Matrices and Their Singular Values”, J. Funct. Anal., 270:4 (2016), 1479–1500  crossref  mathscinet  zmath  isi  scopus
    3. Bogoya J.M. Boettcher A. Maximenko E.A., “From convergence in distribution to uniform convergence”, Bol. Soc. Mat. Mex., 22:2, SI (2016), 695–710  crossref  mathscinet  zmath  isi  scopus
    4. Garoni C., Serra-Capizzano S., “Spectral Distribution Results Beyond the Algebra Generated By Variable-Coefficient Toeplitz Sequences: the Glt Approach”, J. Fourier Anal. Appl., 24:2 (2018), 506–524  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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