De la Vallée Poussin problem in the kernel of the convolution operator on the half-plane

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki

Valentin V Napalkov¹  Karina R Zimens² 

[1] Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences;Ufa State Aviation Technical University;

关键词: convolution operator;    de la vallée poussin problem;    multiple interpolation;   

DOI  :  10.14498/vsgtu1355

来源: DOAJ

【 摘 要 】

We consider the multipoint de la Vallée Poussin (interpolational) problem in the half-plane $D$, $D=\{z \, :\, \mathop{\mathrm{Re}} z0\}$. Let $\psi(z)\in H(D)$; $\mu_1$, $\mu_2$,~$\ldots \in D$ be the positive zero points of this function and let the boundary of domain $D$ contain their limit. Also, we assume that $\mu_k$ is of $s_k$ multiplicity, $k=1, 2, \dots$. Let us set $M_{\varphi}$ an operator of convolution with the characteristic function $\varphi(z)$. Taking an arbitrary sequence $a_{kj},$ $j=0, 1, \ldots, s_k-1$ we should ask: is there a function $u(z) \in \mathop{\mathrm{Ker}}M_\varphi$ that provides the relation $u^{(j)}(\mu_{k})=a_{kj},$ $j=0, 1,\dots,s_k-1$? We assume the operator characteristic function to be of completely regular growth. The solvability conditions for the multipoint de la Vallée Poussin problem in the half-plain and in the bounded convex domains are obtained.

【 授权许可】

Unknown