Geodesic
On Fourier Series in Generalized Eigenfunctions of a Discrete Sturm-Liouville Operator
Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 90-93

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For semicontinuous summation methods generated by $\Lambda=\{\lambda_{n}(h)\}$ ($n=0,1,\dots$; $h>0$) of Fourier series in eigenfunctions of a discrete Sturm–Liouville operator of class $\mathcal{B}$, some results on the uniform a.e. behavior of $\Lambda$-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 $\lambda_{n}(h)=\exp(-u^{\alpha}(n)h)$ are obtained. An application to a generalized heat equation is given.
Keywords: Fourier series, discrete operator, Sturm–Liouville operator, eigenfunctions, semicontinuous summation methods, generalized heat equation, Jacobi polynomials, Pollaczek polynomials, loaded Gegenbauer polynomials.
Mots-clés : orthogonal polynomials 
@article{FAA_2018_52_2_a9,
     author = {B. P. Osilenker},
     title = {On {Fourier} {Series} in {Generalized} {Eigenfunctions} of a {Discrete} {Sturm-Liouville} {Operator}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {90--93},
     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a9/}
}
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B. P. Osilenker. On Fourier Series in Generalized Eigenfunctions of a Discrete Sturm-Liouville Operator. Funkcionalʹnyj analiz i ego priloženiâ, Tome 52 (2018) no. 2, pp. 90-93. http://geodesic.mathdoc.fr/item/FAA_2018_52_2_a9/