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FIXED POINT THEOREM FOR AN INFINITE TOEPLITZ MATRIX
Part of:
Combinatorial probability
Convergence and divergence of infinite limiting processes
Special matrices
Inversion theorems
Published online by Cambridge University Press: 09 November 2020
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
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 104 , Issue 1 , August 2021 , pp. 108 - 117
- Copyright
- © 2020 Australian Mathematical Publishing Association Inc.
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