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Spectral Self-Affine Measures on the Generalized Three Sierpinski Gasket

Spectral Self-Affine Measures on the Generalized Three Sierpinski Gasket

Year:    2015

Analysis in Theory and Applications, Vol. 31 (2015), Iss. 4 : pp. 394–406

Abstract

The self-affine measure μM,D associated with an iterated function system{ϕd(x)=M1(x+d)}dD is uniquely determined. It only depends upon an expanding matrix M and a finite digit set D. In the present paper we give some sufficient conditions for finite and infinite families of orthogonal exponentials. Such research is necessary to further understand the non-spectral and spectral of μM,D. As an application, we show that the L2(μM,D) space has infinite families of orthogonal exponentials on the generalized three Sierpinski gasket. We then consider the spectra of a class of self-affine measures which extends several known conclusions in a simple manner.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/ata.2015.v31.n4.5

Analysis in Theory and Applications, Vol. 31 (2015), Iss. 4 : pp. 394–406

Published online:    2015-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    Compatible pair orthogonal exponentials spectral measure.

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