Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

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

Spectral property of the planar self-affine measures with three-element digit sets AbstractLet the self-affine measure μM,D{\mu_{M,D}} be generated by an expanding real matrix M=diag⁡(ρ1-1,ρ2-1){M=\operatorname{diag}(\rho_{1}^{-1},\rho_{2}^{-1})} and an integer digit setD={(0,0)t,(α1,α2)t,(β1,β2)t}{D=\{(0,0)^{t},(\alpha_{1},\alpha_{2})^{t},(\beta_{1},\beta_{2})^{t}\}} with α1⁢β2-α2⁢β1≠0{\alpha_{1}\beta_{2}-\alpha_{2}\beta_{1}\neq 0}. In this paper, the sufficient and necessary conditions for L2⁢(μM,D){L^{2}(\mu_{M,D})} to contain an infinite orthogonal set of exponential functions are given. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Forum Mathematicum de Gruyter

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

Forum Mathematicum , Volume 32 (3): 9 – May 1, 2020

Loading next page...
 
/lp/de-gruyter/spectral-property-of-the-planar-self-affine-measures-with-three-8iSJqawkfR

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© 2021 Walter de Gruyter GmbH, Berlin/Boston
ISSN
0933-7741
eISSN
1435-5337
DOI
10.1515/forum-2019-0223
Publisher site
See Article on Publisher Site

Abstract

AbstractLet the self-affine measure μM,D{\mu_{M,D}} be generated by an expanding real matrix M=diag⁡(ρ1-1,ρ2-1){M=\operatorname{diag}(\rho_{1}^{-1},\rho_{2}^{-1})} and an integer digit setD={(0,0)t,(α1,α2)t,(β1,β2)t}{D=\{(0,0)^{t},(\alpha_{1},\alpha_{2})^{t},(\beta_{1},\beta_{2})^{t}\}} with α1⁢β2-α2⁢β1≠0{\alpha_{1}\beta_{2}-\alpha_{2}\beta_{1}\neq 0}. In this paper, the sufficient and necessary conditions for L2⁢(μM,D){L^{2}(\mu_{M,D})} to contain an infinite orthogonal set of exponential functions are given.

Journal

Forum Mathematicumde Gruyter

Published: May 1, 2020

Keywords: Self-affine measure; spectral measure; spectrum; orthogonal exponential functions; 28A80; 42C05; 46C05

References