The sum 1/(n w(n)) converging is necessary and sufficient for an increasing w(n) to be an a.e. unconditional convergence Weyl multiplier for arbitrary wavelet-type systems, and log n is optimal for rearranged systems.
On UC-multipliers for multiple trigonometric systems
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We investigate the class of sequences $w(n)$ that can serve as almost-everywhere convergence Weyl multipliers for all rearrangements of multiple trigonometric systems. We show that any such sequence must satisfy the bounds $\log n\lesssim w(n)\lesssim\log^2 n$. Our main result establishes a general equivalence principle between one-dimensional and multidimensional trigonometric systems, which allows one to extend certain estimates known for the one-dimensional case to higher dimensions.
fields
math.CA 1years
2026 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
Quantitative estimates for the absolute convergence of wavelet-type series
The sum 1/(n w(n)) converging is necessary and sufficient for an increasing w(n) to be an a.e. unconditional convergence Weyl multiplier for arbitrary wavelet-type systems, and log n is optimal for rearranged systems.