Analysis of μ  M, D  ‐orthogonal exponentials for the planar four‐element digit sets | Zendy

Li JianLin | Zendy

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Analysis of μ M, D ‐orthogonal exponentials for the planar four‐element digit sets

Author(s) -

Li JianLin

Publication year - 2014

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201300009

Subject(s) - mathematics , affine transformation , numerical digit , measure (data warehouse) , planar , simple (philosophy) , exponential function , set (abstract data type) , element (criminal law) , affine space , matrix (chemical analysis) , discrete mathematics , combinatorics , identity matrix , class (philosophy) , identity (music) , pure mathematics , arithmetic , mathematical analysis , computer science , eigenvalues and eigenvectors , artificial intelligence , philosophy , materials science , computer graphics (images) , database , law , acoustics , composite material , epistemology , quantum mechanics , political science , programming language , physics

The self‐affine measure μ M , Dis a unique probability measure satisfying the self‐affine identity with equal weight. It only depends upon an expanding matrix M and a finite digit set D . In this paper we study the question of when theL 2 ( μ M , D ) ‐space has infinite families of orthogonal exponentials. Such research is necessary to further understanding the spectrality of μ M , D . For a class of planar four‐element digit sets, we present several methods to deal with this question. The application of each method is also given, which extends the known results in a simple manner.

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