Polyorthogonalization in Pre-Hilbert Spaces
For a set of measure and the corresponding scalar products, we define multiple analogues of the Gram determinants and matrices. With their help, we found criteria of uniqueness and explicit form of polyorthogonal functions, obtained as a result of the described process of polyorthogonalization of li...
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| Veröffentlicht in: | Lobachevskii journal of mathematics 2023-04, Vol.44 (4), p.1506-1512 |
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| container_issue | 4 |
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| container_title | Lobachevskii journal of mathematics |
| container_volume | 44 |
| creator | Starovoitov, A. P. Kechko, E. P. |
| description | For a set of measure
and the corresponding scalar products, we define multiple analogues of the Gram determinants and matrices. With their help, we found criteria of uniqueness and explicit form of polyorthogonal functions, obtained as a result of the described process of polyorthogonalization of linearly independent systems
in the pre-Hilbert function spaces generated by the measures
. Our results generalize Schmidt’s theorem about orthogonalization. |
| doi_str_mv | 10.1134/S1995080223040273 |
| format | Article |
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| identifier | ISSN: 1995-0802 |
| ispartof | Lobachevskii journal of mathematics, 2023-04, Vol.44 (4), p.1506-1512 |
| issn | 1995-0802 1818-9962 |
| language | eng |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Algebra Analysis Determinants Function space Geometry Hilbert space Mathematical Logic and Foundations Mathematics Mathematics and Statistics Probability Theory and Stochastic Processes |
| title | Polyorthogonalization in Pre-Hilbert Spaces |
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