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On Fourier Series in Generalized Eigenfunctions of a Discrete Sturm–Liouville Operator

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Abstract

For semicontinuous summation methods generated by Λ = {λn(h)} (n = 0, 1, 2,...; h > 0) of Fourier series in eigenfunctions of a discrete Sturm–Liouville operator of class B, some results on the uniform a.e. behavior of Λ-means are obtained. The results are based on strong- and weak-type estimates of maximal functions. As a consequence, some statements on the behavior of the summation methods generated by the exponential means λn(h) = exp(−uα(n)h) are obtained. An application to a generalized heat equation is given.

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References

  1. Yu. M. Berezansky, Expansions in Eigenfunctions of Self-Adjoint Operators, Amer. Math. Soc., Providence, RI, 1968.

    Book  Google Scholar 

  2. A. D. Nakhman and B. P. Osilenker, Intern. Journ. of Experimental Education, 2014, No. 3, 75–80.

    Google Scholar 

  3. E. M. Nikishin and V. N. Sorokin, Rational Approximation and Orthogonality, Trans. Math. Monographs, vol. 92, Amer. Math. Soc., Providence, RI, 1991.

  4. B. P. Osilenker, Izv. Vyssh. Uchebn. Zaved., 2010, No. 2, 53–65.

    MathSciNet  Google Scholar 

  5. B. P. Osilenker and A. D. Nakhman, Vestnik MGSU, 2014, No. 10, 54–63.

    Article  Google Scholar 

  6. G. Szegö, Orthogonal Polynomials, Amer. Math. Soc. Colloquium Publications, vol. 23, Amer. Math. Soc., Providence, RI, 1939.

  7. S. Bochner, in: Proc. Conf. Diff. Equation, Maryland, 1955, 23–48.

    Google Scholar 

  8. G. Gasper, Ann. of Math., 95:2 (1972), 266–280.

    Article  Google Scholar 

  9. P. Nevai, in: Progress in Approximation Theory, Springer-Verlag, New York–Berlin, 1992, 79–104.

    Book  Google Scholar 

  10. P. Nevai, Orthogonal Polynomials, Mem. Amer. Math. Soc., vol. 18, Number 213, Amer. Math. Soc., Providence, RI, 1979.

  11. W. Van Assche, in: Orthogonal Polynomials: Theory and Practice, Kluwer, Dordrecht, 1990, 435–462.

    Book  Google Scholar 

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Authors and Affiliations

  1. Moscow State University of Civil Engineering Moscow, 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, Vol. 52, No. 2, pp. 90–93, 2018

Original Russian Text Copyright © by B. P. Osilenker

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Osilenker, B.P. On Fourier Series in Generalized Eigenfunctions of a Discrete Sturm–Liouville Operator. Funct Anal Its Appl 52, 154–157 (2018). https://doi.org/10.1007/s10688-018-0223-6

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  • DOI: https://doi.org/10.1007/s10688-018-0223-6

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