Polyorthogonal systems of functions

A. P. Starovoitov

Problemy fiziki, matematiki i tehniki, no. 1 (2022), pp. 89-93.

Résumé

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.

Détail

Keywords: Padé approximations, normal index, perfect system, Gram determinant.
Mots-clés : polyorthogonal polynomials

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