The dual spectral set conjecture

Author:
Steen Pedersen

Translated by:

Journal:
Proc. Amer. Math. Soc. **132** (2004), 2095-2101

MSC (2000):
Primary 42A99, 42C99, 51M04, 52C99

Published electronically:
February 6, 2004

MathSciNet review:
2053982

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Abstract | References | Similar Articles | Additional Information

Abstract: Suppose that where are real numbers such that and The union is not assumed to be disjoint. It is shown that the translates , , tile the real line for some bounded measurable set if and only if the exponentials , , form an orthogonal basis for some bounded measurable set

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Additional Information

**Steen Pedersen**

Affiliation:
Department of Mathematics, Wright State University, Dayton, Ohio 45435

Email:
steen@math.wright.edu

DOI:
https://doi.org/10.1090/S0002-9939-04-07403-9

Keywords:
Fourier basis,
non-harmonic Fourier series,
tiling,
spectral set,
spectral pair

Received by editor(s):
April 15, 2003

Published electronically:
February 6, 2004

Communicated by:
David R. Larson

Article copyright:
© Copyright 2004
American Mathematical Society