Spectral property of the Bernoulli convolutions
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AbstractFor 0 < p < 1, let mu rho be the Bernoulli convolution associated with p. Jorgensen and Pedersen [P. Jorgensen, S. Pedersen, Dense analytic subspaces in fractal L-2-spaces, J. Anal. Math. 75 (1998) 185-228] proved that if rho = 1/q where q is an even integer, then L-2(mu rho) has an exponential orthonormal basis. We show that for any 0 < p < 1, L-2(mu rho) contains an infinite orthonormal set of exponential functions if and only if p is the nth root of a fraction p/q where p is an odd integer and q is an even integer. (C) 2008 Elsevier Inc. All rights reserved.
All Author(s) ListHu TY, Lau KS
Journal nameAdvances in Mathematics
Detailed descriptionTo ORKTS:

Year2008
Month10
Day1
Volume Number219
Issue Number2
PublisherACADEMIC PRESS INC ELSEVIER SCIENCE
Pages554 - 567
ISSN0001-8708
eISSN1090-2082
LanguagesEnglish-United Kingdom
KeywordsBernoulli convolution; minimal polynomial; orthogonality; self-similarity; spectral set
Web of Science Subject CategoriesMathematics; MATHEMATICS

Last updated on 2021-08-01 at 00:32