Roots of complex polynomials and Weyl-Heisenberg frame sets

Authors:
Peter G. Casazza and Nigel J. Kalton

Journal:
Proc. Amer. Math. Soc. **130** (2002), 2313-2318

MSC (1991):
Primary 30C15, 11C08, 42C15, 46C05

DOI:
https://doi.org/10.1090/S0002-9939-02-06352-9

Published electronically:
January 17, 2002

MathSciNet review:
1896414

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Abstract | References | Similar Articles | Additional Information

Abstract: A Weyl-Heisenberg frame for is a frame consisting of modulates and translates , , of a fixed function , for . A fundamental question is to explicitly represent the families so that is a frame for . We will show an interesting connection between this question and a classical problem of Littlewood in complex function theory. In particular, we show that classifying the characteristic functions for which is a frame for is equivalent to classifying the integer sets so that does not have any zeroes on the unit circle in the plane.

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Additional Information

**Peter G. Casazza**

Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211

Email:
pete@math.missouri.edu

**Nigel J. Kalton**

Affiliation:
Department of Mathematics, University of Missouri-Columbia, Columbia, Missouri 65211

Email:
nigel@math.missouri.edu

DOI:
https://doi.org/10.1090/S0002-9939-02-06352-9

Received by editor(s):
February 28, 2000

Received by editor(s) in revised form:
February 16, 2001

Published electronically:
January 17, 2002

Additional Notes:
The first author was supported by NSF DMS 9706108 and the second author by NSF DMS 9870027

Communicated by:
David R. Larson

Article copyright:
© Copyright 2002
American Mathematical Society