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pro vyhledávání: '"Gorbachev D"'
For the kernel $B_{\kappa,a}(x,y)$ of the $(\kappa,a)$-generalized Fourier transform $\mathcal{F}_{\kappa,a}$, acting in $L^{2}(\mathbb{R}^{d})$ with the weight $|x|^{a-2}v_{\kappa}(x)$, where $v_{\kappa}$ is the Dunkl weight, we study the important
Externí odkaz:
http://arxiv.org/abs/2210.15730
We consider direct and inverse Jacobi transforms with measures $d\mu(t)=2^{2\rho}(\sinh t)^{2\alpha+1}(\cosh t)^{2\beta+1}\,dt$ and $d\sigma(\lambda)=(2\pi)^{-1}\bigl|\frac{2^{\rho-i\lambda}\Gamma(\alpha+1)\Gamma(i\lambda)} {\Gamma((\rho+i\lambda)/2)
Externí odkaz:
http://arxiv.org/abs/2112.05802
In this paper we study direct and inverse approximation inequalities in $L^{p}(\mathbb{R}^{d})$, $1
Externí odkaz:
http://arxiv.org/abs/1912.03743
We study the uncertainty principles related to the generalized Logan problem in $\mathbb{R}^{d}$. Our main result provides the complete solution of the following problem: for a fixed $m\in \mathbb{Z}_{+}$, find \[ \sup\{|x|\colon (-1)^{m}f(x)>0\}\cdo
Externí odkaz:
http://arxiv.org/abs/1904.11328
Autor:
Gorbachev, D. V., Ivanov, V. I.
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 direct and inverse theorems of approximation theory, and some inequalitie
Externí odkaz:
http://arxiv.org/abs/1812.04946
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-Littlewood-Sobolev type inequality and weighted week $(L^1, L^q)$ estimate
Externí odkaz:
http://arxiv.org/abs/1708.09733
We prove that the spherical mean value of the Dunkl-type generalized translation operator $\tau^y$ is a positive $L^p$-bounded generalized translation operator $T^t$. As application, we prove the Young inequality for a convolution defined by $T^t$, t
Externí odkaz:
http://arxiv.org/abs/1703.06830
Akademický článek
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Autor:
Gorbachev, D. V.1 (AUTHOR) dvg4mail@gmail.com, Ivanov, V. I.1 (AUTHOR)
Publikováno v:
Mathematical Notes. Feb2023, Vol. 113 Issue 1/2, p143-148. 6p.
Autor:
Gorbachev, D., Tikhonov, S.
We prove two-sided inequalities between the integral moduli of smoothness of a function on $\mathbb{R}^d/\mathbb{T}^d$ and the weighted tail-type integrals of its Fourier transform/series. Sharpness of obtained results in particular is given by the e
Externí odkaz:
http://arxiv.org/abs/1204.4392