On uniqueness sets and coefficients of multiple Walsh series converging over cubes
Abstract
We study problems on uniqueness sets ($U$-sets) for multiple Walsh series converging over cubes and the properties of the coefficients of such series. New broad classes of $U$-sets are constructed. In particular, it is proved that hyperplanes parallel to the coordinate ones are $U$-sets. For the coefficients of multiple Walsh series converging over cubes, both the index sets on which they can be made arbitrarily large and the index sets on which these coefficients tend to zero are described.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
Approximation Theory and Sequence Spaces
p-Adic Analysis and Mathematical Physics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 28 February 2026
- Language
- EN
- Document type
- Preprint