Interpolation Khrushchev-type formulas for structured operators, inequalities and asymptotic relations
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866929420115116032 |
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| author | Sakhnovich, Alexander |
| author_facet | Sakhnovich, Alexander |
| contents | We show that interpolation results in the $S$-nodes theory may be considered as Khrushchev-type formulas. If separation of the well-known Verblunsky (Schur) coefficients occurs in Khrushchev formulas, the separation of the so the called new Verblunsky-type coefficients occurs in the interpolation formulas of the $S$-nodes theory. General asymptotic inequalities (and equalities) for the $S$-nodes, with application to the block Hankel matrices, are derived using this approach. Another asymptotic inequality, needed in the proofs and important in itself, is derived in Appendix B. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_10122 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interpolation Khrushchev-type formulas for structured operators, inequalities and asymptotic relations Sakhnovich, Alexander Classical Analysis and ODEs Functional Analysis Spectral Theory 15B05, 41A05, 42C05, 47A48 We show that interpolation results in the $S$-nodes theory may be considered as Khrushchev-type formulas. If separation of the well-known Verblunsky (Schur) coefficients occurs in Khrushchev formulas, the separation of the so the called new Verblunsky-type coefficients occurs in the interpolation formulas of the $S$-nodes theory. General asymptotic inequalities (and equalities) for the $S$-nodes, with application to the block Hankel matrices, are derived using this approach. Another asymptotic inequality, needed in the proofs and important in itself, is derived in Appendix B. |
| title | Interpolation Khrushchev-type formulas for structured operators, inequalities and asymptotic relations |
| topic | Classical Analysis and ODEs Functional Analysis Spectral Theory 15B05, 41A05, 42C05, 47A48 |
| url | https://arxiv.org/abs/2407.10122 |