Variable-coefficient Toeplitz Matrices with Symbols beyond the Wiener Algebra
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.
Mathematics Subject Classification (2000)Primary 47B35 Secondary 15A60 65F35.
KeywordsToeplitz matrix variable coefficients matrix norm
Unable to display preview. Download preview PDF.
- D. Fasino and S. Serra Capizzano, From Toeplitz matrix sequences to zero distribution of orthogonal polynomials, Fast Algorithms for Structured Matrices: Theory and Applications (South Hadley, MA, 2001), 329–339, Contemp. Math., 323, Amer. Math. Soc., Providence, RI 2003.Google Scholar
- V. Rabinovich, S. Roch, and B. Silbermann, Limit Operators and Their Applications in Operator Theory, Operator Theory: Advances and Applications, 150, Birkhäuser Verlag, Basel 2004.Google Scholar
- O.N. Zabroda, Generalized Convolution Operators and Asymptotic Spectral Theory, Dissertation, TU Chemnitz 2006.Google Scholar