SPECTRUM OF A SELF-AFFINE MEASURE WITH FOUR-ELEMENT DIGIT SET

M. Megala and Srijanani Anurag Prasad ()
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M. Megala: Department of Mathematics and Statistics, Indian Institute of Technology Tirupati, Tirupati, Andhra Pradesh, India
Srijanani Anurag Prasad: Department of Mathematics and Statistics, Indian Institute of Technology Tirupati, Tirupati, Andhra Pradesh, India

FRACTALS (fractals), 2022, vol. 30, issue 04, 1-5

Abstract: Let D = {(00 ), (10 ), (01 ), ( − 1 − 1 )} and M ∈ M2(ℤ) be an expansive matrix. In this paper, we have proved that there exists Λ such that the set ℰΛ := {e2πi〈λ,x〉 : λ ∈ Λ} is an orthonormal basis of L2(μ M,D) for a matrix which has all even entries. Also, we have found a spectrum Λ of L2(μ M,D) for some specific M and D.

Keywords: Iterated Function System; Self-Affine Measure; Spectrum; Compatible Pair; Digit Set (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22500876

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