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FIXED POINT THEOREM FOR AN INFINITE TOEPLITZ MATRIX

Part of: Special matrices Combinatorial probability Inversion theorems Convergence and divergence of infinite limiting processes

Published online by Cambridge University Press:  09 November 2020

VYACHESLAV M. ABRAMOV Open the ORCID record for VYACHESLAV M. ABRAMOV [Opens in a new window]
VYACHESLAV M. ABRAMOV*
Affiliation:
24 Sagan Drive, Cranbourne North, Victoria3977, Australia
*
e-mail: [email protected]
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Abstract

For an infinite Toeplitz matrix T with nonnegative real entries we find the conditions under which the equation $\boldsymbol {x}=T\boldsymbol {x}$ , where $\boldsymbol {x}$ is an infinite vector column, has a nontrivial bounded positive solution. The problem studied in this paper is associated with the asymptotic behaviour of convolution-type recurrence relations and can be applied to problems arising in the theory of stochastic processes and other areas.

Keywords

combinatorial probabilityfixed point theoremgenerating functionsTauberian theoremsToeplitz matrix

MSC classification

Primary: 15B05: Toeplitz, Cauchy, and related matrices
Secondary: 40E05: Tauberian theorems, general 40A30: Convergence and divergence of series and sequences of functions 60C99: None of the above, but in this section
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 1 , August 2021 , pp. 108 - 117
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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