S. Tikhonov

activity

20172025

most citedRiesz potential and maximal function for Dunkl transform

8 citations · 13 across the 4 of their papers we have counts for

collaborators

6 papers

math.CA2025

Chebyshev systems and Sturm oscillation theory for discrete polynomials

D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov

We prove an analogue of Chebyshev's alternation theorem for linearly independent discrete functions $Φ_{n} = {φ_{k}}_{k = 1}^{n}$ on the interval $[0,q]_{\scriptscriptstyle\mathbb{Z}}=[0,q…

math.CA2022★ 2 cited

On the kernel of the $(κ, a)$ -generalized Fourier transform

D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov

For the kernel $B_{κ, a} (x, y)$ of the $(κ, a)$ -generalized Fourier transform $F_{κ, a}$ , acting in $L^{2} (R^{d})$ with the weight $∣ x ∣^{a - 2} v_{κ} (x)$ , where $v_{κ}$ is…

math.CA2021

Logan's problem for Jacobi transform

D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov

We consider direct and inverse Jacobi transforms with measures $d μ (t) = 2^{2 ρ} (sinh t)^{2 α + 1} (cosh t)^{2 β + 1} d t$ and $dσ(λ)=(2π)^{-1}\bigl|\frac{2^{ρ-iλ}Γ(α+1)Γ(iλ)} {Γ((ρ+iλ)/2)Γ…

math.CA2019★ 3 cited

Smoothness of functions vs. smoothness of approximation processes

Yu. Kolomoitsev, S. Tikhonov

We provide a comprehensive study of interrelations between different measures of smoothness of functions on various domains and smoothness properties of approximation processes. Tw…

math.CA2018

Sharp Remez inequality

S. Tikhonov, P. Yuditskii

Let an algebraic polynomial $P_{n} (ζ)$ of degree $n$ be such that $∣ P_{n} (ζ) ∣ \leq 1$ for $ζ \in E \subset T$ and $∣ E ∣ \geq 2 π - s$ . We prove the sharp Remez inequality $$ \sup_{ζ\in\m…

math.CA2017★ 8 cited

Riesz potential and maximal function for Dunkl transform

D. V. Gorbachev, V. I. Ivanov, S. Yu. Tikhonov

We study weighted $(L^{p}, L^{q})$ -boundedness properties of Riesz potentials and fractional maximal functions for the Dunkl transform. In particular, we obtain the weighted Hardy-Litt…

Chebyshev systems and Sturm oscillation theory for discrete polynomials

On the kernel of the (κ,a)-generalized Fourier transform

Logan's problem for Jacobi transform

Smoothness of functions vs. smoothness of approximation processes

Sharp Remez inequality

Riesz potential and maximal function for Dunkl transform

On the kernel of the $(κ, a)$ -generalized Fourier transform