On the Fourier orthonormal bases of Cantor–Moran measures
| Autor: | Liu He, Xing-Gang He |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Sequence 010102 general mathematics 01 natural sciences Measure (mathematics) Convolution Combinatorics symbols.namesake Distribution (mathematics) Fourier transform 0103 physical sciences symbols Orthonormal basis 010307 mathematical physics 0101 mathematics Borel probability measure Analysis Mathematics Probability measure |
| Zdroj: | Journal of Functional Analysis. 272:1980-2004 |
| ISSN: | 0022-1236 |
| DOI: | 10.1016/j.jfa.2016.09.021 |
| Popis: | Let { d n , p n } n = 1 ∞ be a sequence of integers so that 0 d n p n for n ≥ 1 . The infinite convolution of probability measures with finite support and equal distribution μ { p n } , { d n } : = δ p 1 − 1 { 0 , d 1 } ⁎ δ ( p 1 p 2 ) − 1 { 0 , d 2 } ⁎ ⋯ is a Borel probability measure (Cantor–Moran measure). In this paper we study the existence of Fourier basis for L 2 ( μ { p n } , { d n } ) , i.e., find a discrete set Λ such that E Λ = { e − 2 π i λ x : λ ∈ Λ } is an orthonormal basis for L 2 ( μ { p n } , { d n } ) . We give some sufficient conditions for this aim and some examples to explain the theory. |
| Databáze: | OpenAIRE |
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