Abstract
Sequences of so-called variable-coefficient Toeplitz matrices arise in many problems, including the discretization of ordinary differential equations with variable coefficients. Such sequences are known to be bounded if the generating function satisfies a condition of the Wiener type, which is far away from the minimal requirement in the case of constant coefficients. The purpose of this paper is to uncover some phenomena beyond the Wiener condition. We provide counterexamples on the one hand and prove easy-to-check sufficient conditions for boundedness on the other.
This work was partially supported by CONACYT project U46936-F, Mexico.
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In Memory of Georg Heinig
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Böttcher, A., Grudsky, S. (2010). Variable-coefficient Toeplitz Matrices with Symbols beyond the Wiener Algebra. In: Bini, D.A., Mehrmann, V., Olshevsky, V., Tyrtyshnikov, E.E., van Barel, M. (eds) Numerical Methods for Structured Matrices and Applications. Operator Theory: Advances and Applications, vol 199. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8996-3_8
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DOI: https://doi.org/10.1007/978-3-7643-8996-3_8
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