The Existence of Infinite Orthogonal Sets of Moran Measures with Three-Element Digit Sets
- 1 January 2023
- journal article
- Published by Hans Publishers in Pure Mathematics
- Vol. 13 (02), 354-363
- https://doi.org/10.12677/pm.2023.132039
Abstract
For n ≥ 1, let Pn > 1 and Dn ={ 0,an,bn} ⊂ℤ, where an < bn < pn. In this paper we study the existence of infinite orthogonal exponential sets of moran measures which is generated by the sequence of integers {pn}n=1∞ and the sequence of number sets {Dn}n=1∞. We obtain the necessary and sufficient conditions for infinite convolution μ to have infinite orthogonal exponential sets, this provides a good idea for constructing the spectrum of this function space.Keywords
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