Spectral properties of certain Moran measures with consecutive and collinear digit sets
| Autor: | Xin-Han Dong, Yu-Min Li, Hai-Hua Wu |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
General Mathematics 010102 general mathematics Spectral properties Mathematical analysis Spectrum (functional analysis) 01 natural sciences Spectral measure Numerical digit symbols.namesake Fourier transform 0103 physical sciences symbols 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Forum Mathematicum. 32:683-692 |
| ISSN: | 1435-5337 0933-7741 |
| DOI: | 10.1515/forum-2019-0248 |
| Popis: | Let the 2 × 2 {2\times 2} expanding matrix R k {R_{k}} be an integer Jordan matrix, i.e., R k = diag ( r k , s k ) {R_{k}=\operatorname{diag}(r_{k},s_{k})} or R k = J ( p k ) {R_{k}=J(p_{k})} , and let D k = { 0 , 1 , … , q k - 1 } v {D_{k}=\{0,1,\ldots,q_{k}-1\}v} with v = ( 1 , 1 ) T {v=(1,1)^{T}} and 2 ≤ q k ≤ p k , r k , s k {2\leq q_{k}\leq p_{k},r_{k},s_{k}} for each natural number k. We show that the sequence of Hadamard triples { ( R k , D k , C k ) } {\{(R_{k},D_{k},C_{k})\}} admits a spectrum of the associated Moran measure provided that lim inf k → ∞ 2 q k ∥ R k - 1 ∥ < 1 {\liminf_{k\to\infty}2q_{k}\lVert R_{k}^{-1}\rVert . |
| Databáze: | OpenAIRE |
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