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FIXED POINT THEOREM FOR AN INFINITE TOEPLITZ MATRIX

Published online by Cambridge University Press:  09 November 2020

VYACHESLAV M. ABRAMOV*
Affiliation:
24 Sagan Drive, Cranbourne North, Victoria3977, Australia

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.

Type
Research Article
Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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