arXiv subjects

Anton Tselishchev

Publications and source records attributed to Anton Tselishchev.

23 records · Page 2Linked to original sources

arXiv2021

Absence of local unconditional structure in spaces of smooth functions on the torus of arbitrary dimension

Consider a finite collection $\{T_1, \ldots, T_J\}$ of differential operators with constant coefficients on $\mathbb{T}^n$ ($n\geq 2$) and the space of smooth functions generated by this collection, namely, the space of functions $f$ such that $T_j f \in C(\mathbb{T}^n)$, $1\leq j\leq J$. We prove that if there are at least two linearly independent operators among their senior parts (relative to some mixed pattern of homogeneity), then this space does not have local unconditional structure. This fact generalizes the previously known result that such spaces are not isomorphic to a complemented subspace of $C(S)$

math.FA↗

arXiv2020

Absence of local unconditional structure in spaces of smooth functions on two-dimensional torus

Consider a finite collection $\{T_1, \ldots, T_J\}$ of differential operators with constant coefficients on $\mathbb{T}^2$ and the space of smooth functions generated by this collection, namely, the space of functions $f$ such that $T_j f \in C(\mathbb{T}^2)$. We prove that under a certain natural condition this space is not isomorphic to a quotient of a $C(S)$-space and does not have a local unconditional structure. This fact generalizes the previously known result that such spaces are not isomorphic to a complemented subspace of $C(S)$.

math.FA↗

arXiv2019

Stability of nearly optimal decompositions in Fourier Analysis

The question of existence is treated for near-minimizers for the distance functional (or $E$-functional in the interpolation terminology) that are stable under the action of certain operators. In particular, stable near-minimizers for the couple $(L^1, L^p)$ are shown to exist when the operator is the projection on wavelets and these wavelets possess only some weak conditions of decay at infinity.

math.CA↗

arXiv2019

Duality in a stability problem for some functionals arising in interpolation theory

By using duality, it is shown that there exist near-minimizers for the distance functionals for the couple $(L^\infty, L^p)$, $1<p<\infty$, that are stable under the action of singular integral operators.

math.FA↗

arXiv2018

Littlewood--Paley characterizations of $\mathrm{BMO}$ and Triebel--Lizorkin spaces

We prove one generalization of the Littlewood--Paley characterization of the $\mathrm{BMO}$ space where the dilations of a Schwartz function are replaced by a family of functions with suitable conditions imposed on them. We also prove that a certain family of Triebel--Lizorkin spaces can be characterized in a similar way.

math.CA↗