Spectral structure and spectral eigenvalue problems of a class of self-similar spectral measures

By Xinggang He, Min Tang, Zhiyi Wu. Journal of Functional Analysis, 2019

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Abstract Let μ be a probability measure with compact support in R . The measure μ is called a spectral measure if there exists a countable set Λ ⊆ R , called a spectrum of μ , such that the family of exponential functions { e − 2 π i λ x : λ ∈ Λ } forms an orthonormal basis for L 2 ( μ ) . In this paper we study the structure of spectra and the real number t such that both Λ and t Λ are spectra for a class of self-similar spectral measures, which have symmetric spectra. Some examples are given to explain our theory.

Subfields: Applied Mathematics, Mathematical Physics

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