V. Ivanov

activity

20172025

most citedRiesz potential and maximal function for Dunkl transform

8 citations · 17 across the 6 of their papers we have counts for

collaborators

7 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

Uncertainty principles for eventually constant sign bandlimited functions

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

We study the uncertainty principles related to the generalized Logan problem in $R^{d}$ . Our main result provides the complete solution of the following problem: for a fix…

math.CA2018

Fractional smoothness in $L^{p}$ with Dunkl weight and its applications

D. V. Gorbachev, V. I. Ivanov

We define fractional power of the Dunkl Laplacian, fractional modulus of smoothness and fractional $K$ -functional in $L^{p}$ -space with the Dunkl weight. As application, we prove dir…

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

Uncertainty principles for eventually constant sign bandlimited functions

Fractional smoothness in Lp with Dunkl weight and its applications

Riesz potential and maximal function for Dunkl transform

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

Fractional smoothness in $L^{p}$ with Dunkl weight and its applications