A necessary and sufficient condition for the finite A mu (M,D) -orthogonality

作者：Li JianLin^*

来源：Science China Mathematics, 2015, 58(12): 2541-2548.

DOI：10.1007/s11425-015-5014-4

• iterated function system
• self-affine measure
• non-spectrality
• digit set

The self-affine measure A mu (M,D) associated with an expanding matrix M a M (n) (a"currency sign) and a finite digit set D aS, a"currency sign (n) is uniquely determined by the self-affine identity with equal weight. The set of orthogonal exponential functions E(I >) := {e(2 pi iaOE (c) I >>, x >) : lambda a I >} in the Hilbert space L (2)(A mu (M,D) ) is simply called A mu (M,D) -orthogonal exponentials. We consider in this paper the finiteness of A mu (M,D) -orthogonality. A necessary and sufficient condition is obtained for the set E(I >) to be a finite A mu (M,D) -orthogonal exponentials. The research here is closely connected with the non-spectrality of self-affine measures.

• 出版日期2015-12
• 单位陕西师范大学