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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]:
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Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 2015, Volume 19, Number 2, Pages 283–292 (Mi vsgtu1355)  

Differential Equations and Mathematical Physics

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

V. V. Napalkova, K. Zimensb

a Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences, Ufa, 450008, Russian Federation
b Ufa State Aviation Technical University, Ufa, 450000, Russian Federation

Abstract: We consider the multipoint de la Vallee Poussin (interpolational) problem in the half-plane $D$, $D=ż  :  \mathop{\mathrm{Re}} z<\alpha,$ $ \alpha>0\}$. 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, $k=1, 2, …$. 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 $u^{(j)}(\mu_{k})=a_{kj},$ $j=0, 1,…,s_k-1$? 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.

Keywords: convolution operator, de la Vallee Poussin problem, multiple interpolation, the half-plane

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00720-а
This work has been supported by the Russian Foundation for Basic Research (project no. 14–01–00720-a).


DOI: https://doi.org/10.14498/vsgtu1355

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Bibliographic databases:

UDC: 517.98
MSC: 58J47, 30D05, 30E10, 46E10
Original article submitted 21/XI/2014
revision submitted – 15/II/2015

Citation: V. V. Napalkov, K. Zimens, “De la Vallee Poussin problem in the kernel of the convolution operator on the half-plane”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:2 (2015), 283–292

Citation in format AMSBIB
\Bibitem{NapZim15}
\by V.~V.~Napalkov, K.~Zimens
\paper De la Vallee Poussin problem in the kernel of the convolution operator on the half-plane
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2015
\vol 19
\issue 2
\pages 283--292
\mathnet{http://mi.mathnet.ru/vsgtu1355}
\crossref{https://doi.org/10.14498/vsgtu1355}
\zmath{https://zbmath.org/?q=an:06968962}
\elib{http://elibrary.ru/item.asp?id=24078305}


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  • Вестник Самарского государственного технического университета. Серия: Физико-математические науки
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