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MATHEMATICS
Polyorthogonal systems of functions
A. P. Starovoitov Francisk Skorina Gomel State University
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
Citation:
A. P. Starovoitov, “Polyorthogonal systems of functions”, PFMT, 2022, no. 1(50), 89–93
Linking options:
https://www.mathnet.ru/eng/pfmt832 https://www.mathnet.ru/eng/pfmt/y2022/i1/p89
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