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

  • Ming-Liang Chen , Jing-Cheng Liu and Juan Su EMAIL logo
Published/Copyright: February 5, 2020

Abstract

Let the self-affine measure μM,D be generated by an expanding real matrix M=diag(ρ1-1,ρ2-1) and an integer digit set D={(0,0)t,(α1,α2)t,(β1,β2)t} with α1β2-α2β10. In this paper, the sufficient and necessary conditions for L2(μM,D) to contain an infinite orthogonal set of exponential functions are given.

MSC 2010: 28A80; 42C05; 46C05

Communicated by Christopher D. Sogge


Award Identifier / Grant number: 11971500

Award Identifier / Grant number: 11831007

Award Identifier / Grant number: 11401053

Award Identifier / Grant number: 17B158

Award Identifier / Grant number: 14C0046

Funding statement: The first author is supported by the NNSF of China (no. 11971500). The second author is supported by the NNSF of China (no. 11831007), by the Hunan Provincial NSF (no. 2019JJ20012) and by the SRF of Hunan Provincial Education Department (no. 17B158). The corresponding author is supported by the NNSF of China (no. 11401053) and by the SRF of Hunan Provincial Education Department (no. 14C0046).

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Received: 2019-08-19
Published Online: 2020-02-05
Published in Print: 2020-05-01

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