Spectral property of the planar self-affine measures with three-element digit sets-Reference-Cited by-同舟云学术

Spectral property of the planar self-affine measures with three-element digit sets

Published:2020-02-05 Issue:3 Volume:32 Page:673-681
ISSN:0933-7741
Container-title:Forum Mathematicum
language:en
Short-container-title:

Author:

Chen Ming-Liang¹,Liu Jing-Cheng²,Su Juan³

Affiliation:

1. School of Mathematics , Sun Yat-Sen University , Guangzhou 510275 , P. R. China

2. Key Laboratory of High Performance Computing and Stochastic Information Processing (Ministry of Education of China) , College of Mathematics and Statistics , Hunan Normal University , Changsha , Hunan 410081 , P. R. China

3. School of Mathematics and Statistics , Changsha University of Science & Technology , Changsha , Hunan 410114 , P. R. China

Abstract

Abstract Let the self-affine measure μ M , D

{\mu_{M,D}}

be generated by an expanding real matrix M = diag ⁡ ( ρ 1 - 1 , ρ 2 - 1 )

{M=\operatorname{diag}(\rho_{1}^{-1},\rho_{2}^{-1})}

and an integer digit set D = { ( 0 , 0 ) t , ( α 1 , α 2 ) t , ( β 1 , β 2 ) t }

{D=\{(0,0)^{t},(\alpha_{1},\alpha_{2})^{t},(\beta_{1},\beta_{2})^{t}\}}

with α 1 ⁢ β 2 - α 2 ⁢ β 1 ≠ 0

{\alpha_{1}\beta_{2}-\alpha_{2}\beta_{1}\neq 0}

. In this paper, the sufficient and necessary conditions for L 2 ⁢ ( μ M , D )

{L^{2}(\mu_{M,D})}

to contain an infinite orthogonal set of exponential functions are given.

Funder

National Natural Science Foundation of China

Scientific Research Foundation of Hunan Provincial Education Department

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/forum-2019-0223/pdf

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