Abstract
Abstract
Let
$\{b_n\}_{n=1}^{\infty }$
be a sequence of integers larger than 1. We will study the harmonic analysis of the equal-weighted Moran measures
$\mu _{\{b_n\},\{{\mathcal D}_n\}}$
with
${\mathcal D}_n=\{0,1,2,\ldots ,q_n-1\}$
, where
$q_n$
divides
$b_n$
for all
$n\geq 1.$
In this paper, we first characterize all the maximal orthogonal sets of
$L^2(\mu _{\{b_n\},\{{\mathcal D}_n\}})$
via a tree mapping. By this characterization, we give some sufficient conditions for the maximal orthogonal set to be an orthonormal basis.
Publisher
Canadian Mathematical Society