6 papers
On exact discretization of the -norm in the space spanned by the first Rademacher functions
Anna Kazakova
We study the exact discretization of the -norm in the space spanned by the first Rademacher functions. It is shown that the sufficient number of nodes for discretization w…
On Lacunarity and Sidon-Type Properties for Subsystems of Characters of Compact Abelian Groups
Anna Kazakova
This paper studies subsystems that generalize Rademacher chaos to arbitrary systems of character of compact abelian groups. The properties of -lacunarity and -Si…
Sidon-type inequalities for -adic analogues of Rademacher chaos
Anna Kazakova
We prove the -Sidon inequality for a system of functions representing the most general extension of the Rademacher -chaos to the -ary case.
On uniqueness sets and coefficients of multiple Walsh series converging over cubes
Anna Kazakova
We study problems on uniqueness sets (-sets) for multiple Walsh series converging over cubes and the properties of the coefficients of such series. New broad classes of -sets…
On multiple null-series in the Walsh system, M- and U- sets
A. D. Kazakova, M. G. Plotnikov
A family of M-sets and null-series for the d-dimensional Walsh system is constructed if we consider convergence over rectangles, cubes, or iterated convergence. Non-empty portions…
On lacunarity and uniqueness for -ary analogues of Rademacher chaos
A. D. Kazakova, M. G. Plotnikov
For two systems of functions that are p-ary analogues of Rademacher chaos, their q-lacunarity is proved and their uniqueness sets are studied.