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Generalized Trace Formula for Polynomials Orthogonal in Continuous-Discrete Sobolev Spaces

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Abstract

In continuous-discrete Sobolev spaces a generalized trace formula for orthogonal polynomials \(\{\widehat{q}_n\}_{n=0}^\infty\) is obtained. The proof of this formula is based on the representation of the Fejér kernel for the system \(\{\widehat{q}_n\}_{n=0}^\infty\). As a consequence, a generalized trace formula for Gegenbauer–Sobolev polynomials in a discrete Sobolev space is obtained.

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  1. Library for Information and Educational Resources, Moscow, Russia

    B. P. Osilenker

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  1. B. P. Osilenker
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Correspondence to B. P. Osilenker.

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Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2020, Vol. 54, pp. 102-105 https://doi.org/10.4213/faa3737.

Translated by B. P. Osilenker

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Osilenker, B.P. Generalized Trace Formula for Polynomials Orthogonal in Continuous-Discrete Sobolev Spaces. Funct Anal Its Appl 54, 310–312 (2020). https://doi.org/10.1134/S0016266320040097

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  • DOI: https://doi.org/10.1134/S0016266320040097

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