Universal Relations in Asymptotic Formulas for Orthogonal Polynomials

Orthogonal polynomials are oscillating functions of as for in the absolutely continuous spectrum of the corresponding Jacobi operator . We show that, irrespective of any specific assumptions on the coefficients of the operator , the amplitude and phase factors in asymptotic formulas for are linked b...

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Published in:Functional analysis and its applications 2021-04, Vol.55 (2), p.140-158
Main Author: Yafaev, D. R.
Format: Article
Language:English
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639/766/189
639/766/530
639/766/747
Analysis
Asymptotic properties
Classical Analysis and ODEs
Functional Analysis
Functions (mathematics)
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Polynomials
Spectral Theory
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description Orthogonal polynomials are oscillating functions of as for in the absolutely continuous spectrum of the corresponding Jacobi operator . We show that, irrespective of any specific assumptions on the coefficients of the operator , the amplitude and phase factors in asymptotic formulas for are linked by certain universal relations found in the paper. Our proofs rely on the study of a time-dependent evolution generated by suitable functions of the operator .
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subjects 14/34
639/766/189
639/766/530
639/766/747
Analysis
Asymptotic properties
Classical Analysis and ODEs
Functional Analysis
Functions (mathematics)
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators (mathematics)
Polynomials
Spectral Theory
title Universal Relations in Asymptotic Formulas for Orthogonal Polynomials
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