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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2022, Issue 1(50), Pages 89–93
DOI: https://doi.org/10.54341/20778708_2022_1_50_89
(Mi pfmt832)
 

MATHEMATICS

Polyorthogonal systems of functions

A. P. Starovoitov

Francisk Skorina Gomel State University
References:
Abstract: This article introduces multiple analogs of determinants and Gram matrices, studies the possibility of constructing polyorthogonal systems of functions using the process of polyorthogonalization of an arbitrary finite subsystem of a linearly independent system of functions $\varphi=\{\varphi_0(x), \varphi_1(x), \dots, \varphi_n(x), \dots\}$ in Pre-Hilbert function spaces generated by measures $\mu_1,\dots,\mu_k$. The proven statements are a generalization of the Gram–Schmidt orthogonalization theorem.
Keywords: Padé approximations, polyorthogonal polynomials, normal index, perfect system, Gram determinant.
Received: 17.12.2021
Document Type: Article
UDC: 517.538.52+517.538.53
Language: Russian
Citation: A. P. Starovoitov, “Polyorthogonal systems of functions”, PFMT, 2022, no. 1(50), 89–93
Citation in format AMSBIB
\Bibitem{Sta22}
\by A.~P.~Starovoitov
\paper Polyorthogonal systems of functions
\jour PFMT
\yr 2022
\issue 1(50)
\pages 89--93
\mathnet{http://mi.mathnet.ru/pfmt832}
\crossref{https://doi.org/10.54341/20778708_2022_1_50_89}
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