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...
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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 |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20459/16706 |
| _version_ | 1818059889593810944 |
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| author | Valentin V Napalkov Karina R Zimens |
| author_facet | Valentin V Napalkov Karina R Zimens |
| author_sort | Valentin V Napalkov |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-10T13:23:42Z |
| format | Article |
| id | doaj.art-b665fdcbf0dd4000862278104e2be4b5 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T13:23:42Z |
| publishDate | 2015-06-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-b665fdcbf0dd4000862278104e2be4b52022-12-22T01:47:16ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812015-06-0119228329210.14498/vsgtu135517879De la Vallée Poussin problem in the kernel of the convolution operator on the half-planeValentin V Napalkov0Karina R Zimens1Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of SciencesUfa State Aviation Technical UniversityWe 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.https://journals.eco-vector.com/1991-8615/article/viewFile/20459/16706convolution operatorde la vallée poussin problemmultiple interpolation |
| spellingShingle | Valentin V Napalkov Karina R Zimens 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 convolution operator de la vallée poussin problem multiple interpolation |
| title | De la Vallée Poussin problem in the kernel of the convolution operator on the half-plane |
| title_full | De la Vallée Poussin problem in the kernel of the convolution operator on the half-plane |
| title_fullStr | De la Vallée Poussin problem in the kernel of the convolution operator on the half-plane |
| title_full_unstemmed | De la Vallée Poussin problem in the kernel of the convolution operator on the half-plane |
| title_short | De la Vallée Poussin problem in the kernel of the convolution operator on the half-plane |
| title_sort | de la vallee poussin problem in the kernel of the convolution operator on the half plane |
| topic | convolution operator de la vallée poussin problem multiple interpolation |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20459/16706 |
| work_keys_str_mv | AT valentinvnapalkov delavalleepoussinprobleminthekerneloftheconvolutionoperatoronthehalfplane AT karinarzimens delavalleepoussinprobleminthekerneloftheconvolutionoperatoronthehalfplane |