De la Vallée Poussin problem in the kernel of the convolution operator on the half-plane
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2015-06-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20459/16706 |
| Summary: | 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. |
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| ISSN: | 1991-8615 2310-7081 |