Interpolation Khrushchev-type formulas for structured operators, inequalities and asymptotic relations
Classical Analysis and ODEs
2024-07-16 v1 Functional Analysis
Spectral Theory
Abstract
We show that interpolation results in the -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 -nodes theory. General asymptotic inequalities (and equalities) for the -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.
Cite
@article{arxiv.2407.10122,
title = {Interpolation Khrushchev-type formulas for structured operators, inequalities and asymptotic relations},
author = {Alexander Sakhnovich},
journal= {arXiv preprint arXiv:2407.10122},
year = {2024}
}
Comments
The results of arXiv:1711.03064, arXiv:1912.05213, and arXiv:2404.02094 are developed much further in this preprint