Geodesic
Generalized Trace Formula for Polynomials\\ Orthogonal in Continuous-Discrete Sobolev Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 54 (2020) no. 4, pp. 102-105

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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.
Mots-clés : orthogonal polynomials, trace formula, Fejér kernel, Sobolev spaces
Keywords: Gegenbauer–Sobolev polynomials, continuous-discrete spaces, symmetric polynomials, Chebyshev polynomials. 
@article{FAA_2020_54_4_a8,
     author = {B. P. Osilenker},
     title = {Generalized {Trace} {Formula} for {Polynomials\\} {Orthogonal} in {Continuous-Discrete} {Sobolev} {Spaces}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {102--105},
     publisher = {mathdoc},
     volume = {54},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2020_54_4_a8/}
}
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B. P. Osilenker. Generalized Trace Formula for Polynomials\\ Orthogonal in Continuous-Discrete Sobolev Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 54 (2020) no. 4, pp. 102-105. http://geodesic.mathdoc.fr/item/FAA_2020_54_4_a8/