On spectral N -Bernoulli measures

Autor: Xin-Rong Dai, Ka-Sing Lau, Xing-Gang He
Rok vydání: 2014
Předmět:
Zdroj: Advances in Mathematics. 259:511-531
ISSN: 0001-8708
DOI: 10.1016/j.aim.2014.03.026
Popis: For 0 ρ 1 and N > 1 an integer, let μ be the self-similar measure defined by μ ( ⋅ ) = ∑ i = 0 N − 1 1 N μ ( ρ − 1 ( ⋅ ) − i ) . We prove that L 2 ( μ ) has an exponential orthonormal basis if and only if ρ = 1 q for some q > 0 and N divides q. The special case is the Cantor measure with ρ = 1 2 k and N = 2 [16] , which was proved recently to be the only spectral measure among the Bernoulli convolutions with 0 ρ 1 [4] .
Databáze: OpenAIRE
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