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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Bibliographic Details
Published in:Functional analysis and its applications 2021-04, Vol.55 (2), p.140-158
Main Author: Yafaev, D. R.
Format: Article
Language:English
Subjects:
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639/766/530
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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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Summary: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 .
ISSN:0016-2663
1573-8485
DOI:10.1134/S0016266321020064