The Cardinality Of Orthogonal Exponentials For Some Self-affine Measure

This paper mainly researches about the non-spectrality of a class of planar self-affine measure with four-element which linear correlation and also about the non-spectrality of a class of planar self-affine measure with four element in R3.The main result of the paper is as followsWhen the non-spectrality of a class of planar self-affine measure with four-element which linear correlation discuss the maximum number of mutually orthogonal exponential functions in L2(μM.D) which is deretated by (M, D).By use of the residue class of4and the α=(1/2,0),it is proved that for the matrix and the digit set some conclusions which is deretated by (M,D).(2)By use the α:=(1/2,1/2,0) and zero set,it is proved that for the matrix M=diag[2p,2p,2p+1](p∈Z) has infinite orthogonal exponentials which is determined by (M. D). And digital setD={0,e1,e2,e3}in which{e1}13=1e1,e2.e3is R3ONB.(3)By use the α:=(1/2,0.0) and zero set,it is proved that for the matrix M=diag[2p,2p+1,2p+1](p∈Z) has infinite orthogonal exponentials which is determined by (M,D).