Anton Tselishchev

activity

20232026

most citedThere are no unconditional Schauder frames of translates in

L^{p} (R)

1 \leq p \leq 2

4 citations · 4 across the 11 of their papers we have counts for

collaborators

12 papers

math.CA2026

There are no unconditional Schauder frames of exponentials in $L^{p}$ spaces, $p \neq = 2$

Nir Lev, Anton Tselishchev

We proved recently that there are no unconditional Schauder frames of exponentials in the space $L^{p} (Ω)$ , $1 \leq p < 2$ , for any set $Ω \subset R^{d}$ of finite measure. For…

math.CA2026

A new example of crystalline-type measure with unit masses and an application to tiling of the real line by translates of a function

Anton Tselishchev

In this note we provide a simple explicit example of a discrete set $Λ \subset R$ of unbounded density such that the Fourier transform of its counting measure $δ_{Λ}$ …

math.CA2026

Gabor unconditional bases and frames in $L^{p} (R)$

Nir Lev, Anton Tselishchev

We consider the following problem: given a set $Λ \subset R \times R$ and $p \neq = 2$ , does there exist a function $g \in L^{p} (R)$ such that the Gabor syste…

math.CA2026

Weighted Chui's conjecture

Evgueni Doubtsov, Anton Tselishchev, Ioann Vasilyev

The goals of this paper are threefold. First, we show that a counterpart of the Newman bound related to the Chui conjecture is valid in the case where the gradient of Coulomb poten…

math.FA2025

Rescaling of unconditional Schauder frames in Hilbert spaces and completely bounded maps

Anton Tselishchev

We prove that if every element $u$ in a Hilbert space $H$ admits a representation as unconditionally convergent series $u = k = 1 \sum \infty ⟨ u, y_{k} ⟩ x_{k},$ then there…

math.CA2025

Unconditional Schauder frames of exponentials and of uniformly bounded functions in $L^{p}$ spaces

Nir Lev, Anton Tselishchev

It is known that there is no unconditional basis of exponentials in the space $L^{p} (Ω)$ , $p \neq = 2$ , for any set $Ω \subset R^{d}$ of finite measure. This is a consequence of a…

math.CA2025

Completeness of sparse, almost integer and finite local complexity sequences of translates in $L^{p} (R)$

Nir Lev, Anton Tselishchev

A real sequence $Λ = {λ_{n}}_{n = 1}^{\infty}$ is called $p$ -generating if there exists a function $g$ whose translates ${g (x - λ_{n})}_{n = 1}^{\infty}$ span the space $L^{p} (R)$ . Whi…

math.CV2024

Reverse Carleson measures for spaces of analytic functions

Evgueni Doubtsov, Anton Tselishchev, Ioann Vasilyev

Let $X$ be a quasi-Banach space of analytic functions in the unit disc and let $q > 0$ . A finite positive Borel measure $μ$ in the closed unit disc $D$ is called…

math.FA2024

Almost Auerbach, Markushevich and Schauder bases in Hilbert and Banach spaces

Anton Tselishchev

For any sequence of positive numbers $(ε_{n})_{n = 1}^{\infty}$ such that $\sum_{n = 1}^{\infty} ε_{n} = \infty$ we provide an explicit simple construction of $(1+\varepsil…

math.CA2024

Schauder frames of discrete translates in $L^{p} (R)$

Nir Lev, Anton Tselishchev

For every $p > (1 + 5) /2$ we construct a uniformly discrete real sequence ${λ_{n}}_{n = 1}^{\infty}$ satisfying $∣ λ_{n} ∣ = n + o (1)$ , a function $g \in L^{p} (R)$ , and conti…

math.CA2023

Schauder frames of discrete translates in $L^{2} (R)$

Nir Lev, Anton Tselishchev

We construct a uniformly discrete sequence ${λ_{1} < λ_{2} < \dots} \subset R$ and functions $g$ and ${g_{n}^{*}}$ in $L^{2} (R)$ , such that every $f \in L^2(\mathbb{R}…

math.CA2023★ 4 cited

There are no unconditional Schauder frames of translates in $L^{p} (R)$ , $1 \leq p \leq 2$

Nir Lev, Anton Tselishchev

It is known that a system formed by translates of a single function cannot be an unconditional Schauder basis in the space $L^{p} (R)$ for any $1 \leq p < \infty$ . To the cont…

There are no unconditional Schauder frames of exponentials in Lp spaces, p=2

A new example of crystalline-type measure with unit masses and an application to tiling of the real line by translates of a function

Gabor unconditional bases and frames in Lp(R)

Weighted Chui's conjecture

Rescaling of unconditional Schauder frames in Hilbert spaces and completely bounded maps

Unconditional Schauder frames of exponentials and of uniformly bounded functions in Lp spaces

Completeness of sparse, almost integer and finite local complexity sequences of translates in Lp(R)

Reverse Carleson measures for spaces of analytic functions

Almost Auerbach, Markushevich and Schauder bases in Hilbert and Banach spaces

Schauder frames of discrete translates in Lp(R)

Schauder frames of discrete translates in L2(R)

There are no unconditional Schauder frames of translates in Lp(R), 1≤p≤2

There are no unconditional Schauder frames of exponentials in $L^{p}$ spaces, $p \neq = 2$

Gabor unconditional bases and frames in $L^{p} (R)$

Unconditional Schauder frames of exponentials and of uniformly bounded functions in $L^{p}$ spaces

Completeness of sparse, almost integer and finite local complexity sequences of translates in $L^{p} (R)$

Schauder frames of discrete translates in $L^{p} (R)$

Schauder frames of discrete translates in $L^{2} (R)$

There are no unconditional Schauder frames of translates in $L^{p} (R)$ , $1 \leq p \leq 2$