Geodesic
On polyorthogonal functions of the first type
Problemy fiziki, matematiki i tehniki, no. 2 (2022), pp. 94-98

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In pre-Hilbert function spaces generated by the measures $\mu_1,\dots,\mu_k$, the process of polyorthogonalization of an arbitrary linearly independent system of functions $\{\varphi_0(x), \varphi_1(x),\dots, \varphi_m(x)\}$ is described, which allows us to introduce the concept of the $n$th polyorthogonal function for an arbitrary multi-index $n$. Necessary and sufficient conditions are found under which this polyorthogonal function is uniquely determined, and its explicit form is described. The main theorem is a multiple analogue of the Gram–Schmidt orthogonalization theorem.
Keywords: linearly independent system, Pre-Hilbert spaces, perfect system, Gram–Schmidt orthogonalization.
Mots-clés : polyorthogonal polynomials 
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     author = {A. P. Starovoitov and A. D. Kovalkova},
     title = {On polyorthogonal functions of the first type},
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     pages = {94--98},
     publisher = {mathdoc},
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     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2022_2_a14/}
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A. P. Starovoitov; A. D. Kovalkova. On polyorthogonal functions of the first type. Problemy fiziki, matematiki i tehniki, no. 2 (2022), pp. 94-98. http://geodesic.mathdoc.fr/item/PFMT_2022_2_a14/