Exponential spectra in L-2 (mu)
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AbstractLet mu be a Borel probability measure with compact support. We consider exponential type orthonormal bases, Riesz bases and frames in L-2(mu). We show that if L-2(mu) admits an exponential frame, then mu must be of pure type. We also classify various mu that admits either kind of exponential bases, in particular, the discrete measures and their connection with integer tiles. By using this and convolution, we construct a class of singularly continuous measures that has an exponential Riesz basis but no exponential orthonormal basis. It is the first of such kind of examples. (C) 2012 Elsevier Inc. All rights reserved.
All Author(s) ListHe XG, Lai CK, Lau KS
Journal nameApplied and Computational Harmonic Analysis
Year2013
Month5
Day1
Volume Number34
Issue Number3
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Pages327 - 338
ISSN1063-5203
eISSN1096-603X
LanguagesEnglish-United Kingdom
KeywordsFourier frames; Integer tiles; Pure types; Riesz bases; Singular measures; Spectra
Web of Science Subject CategoriesMathematics; Mathematics, Applied; MATHEMATICS, APPLIED; Physics; Physics, Mathematical; PHYSICS, MATHEMATICAL

Last updated on 2021-19-01 at 01:16