Affiliation:
1. Key Laboratory of Computing and Stochastic Mathematics (Ministry of Education), School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, P. R. China
Abstract
For a sequence [Formula: see text] of expanding matrices with [Formula: see text] and a sequence [Formula: see text] of finite digit sets with [Formula: see text], the Moran measure [Formula: see text] is defined by the infinite convolution [Formula: see text] and the convergence is in the weak sense. Under some additional assumptions, we show that [Formula: see text] contains an infinite orthogonal set of exponential functions if and only if there exists an infinite subsequence [Formula: see text] of [Formula: see text] such that [Formula: see text] for any [Formula: see text], where [Formula: see text]. This extends the results of [J. L. Li, A necessary and sufficient condition for the finite [Formula: see text]-orthogonality, Sci. China Math. 58 (2015) 2541–2548].
Funder
National Natural Science Foundation of China
Natural Science Foundation of Hunan Province
Publisher
World Scientific Pub Co Pte Ltd