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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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