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A NEW APPROACH TO THE GENERALIZED TRACE FORMULA AND ASYMPTOTICS OF TURÁN’S DETERMINANT FOR POLYNOMIALS WITH ASYMPTOTICALLY N-PERIODIC RECURRENCE COEFFICIENTS

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Abstract

A class of orthonormal polynomials with asymptotically N -periodic recurrence coefficients (APN class) is studied. These polynomials have an essential spectral measure supported on at most N disjoint intervals. By the same approach, for polynomials of class APN, the following two problems are solved: to extend the trace formula and to find an asymptotics of Turán’s determinant for polynomials orthogonal on several intervals.

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  1. Mathematical Department, Moscow State Civil Engineering University, Yaroslavskoe shosse 26, Moscow, 129337, Russia

    B. P. Osilenker

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Osilenker, B.P. A NEW APPROACH TO THE GENERALIZED TRACE FORMULA AND ASYMPTOTICS OF TURÁN’S DETERMINANT FOR POLYNOMIALS WITH ASYMPTOTICALLY N-PERIODIC RECURRENCE COEFFICIENTS. J Math Sci 266, 621–634 (2022). https://doi.org/10.1007/s10958-022-06024-2

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