Spectral radius of the sampling operator with continuous symbol

Author:
Mark C. Ho

Journal:
Proc. Amer. Math. Soc. **129** (2001), 3285-3295

MSC (1991):
Primary 42C15, 47C35, 47C38

DOI:
https://doi.org/10.1090/S0002-9939-01-06057-9

Published electronically:
April 9, 2001

MathSciNet review:
1845004

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Let (where is the -th Fourier coefficient of ) be a bounded measurable function on the unit circle **T**. Consider the operator on whose matrix with respect to the standard basis is given by . In this paper, we give upper and lower bound estimation for , the spectral radius of . Furthermore, we will show that in some cases (for example, if is continuous on **T** and ), the spectral radius of can be computed exactly in terms of roots of the norms of some finite Toeplitz matrices.

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Additional Information

**Mark C. Ho**

Affiliation:
Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung, Taiwan

Email:
hom@math.nsysu.edu.tw

DOI:
https://doi.org/10.1090/S0002-9939-01-06057-9

Received by editor(s):
December 8, 1999

Received by editor(s) in revised form:
March 12, 2000

Published electronically:
April 9, 2001

Communicated by:
David R. Larson

Article copyright:
© Copyright 2001
American Mathematical Society