Abstract
For linear methods of summation of the expansions of generalized functions into a series with respect to the eigenfunctions of a Sturm-Liouville operator one establishes conditions under which the Riemann localization principle holds.
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Literature cited
B. M. Levitan and I. S. Sargsyan, Sturm-Liouville and Dirac Operators [in Russian], Nauka, Moscow (1988).
G. H. Hardy, Divergent Series, Clark Press, Oxford (1949).
V. A. Marchenko, Sturm-Liouville Operators and Their Applications [in Russian], Naukova Dumka, Kiev (1977).
I. G. Izvekov, “The Riemann localization principle for Fourier series in spaces of generalized functions,” Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 2, 5–8 (1986).
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Translated from Ukrainskii Maternaticheskii Zhurnal, Vol. 43, No. 5, pp. 703–706, May, 1991.
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Izvekov, I.G. Localization principle for expansions of generalized functions with respect to the eigenfunctions of the Sturm-Liouville operator on a finite interval. Ukr Math J 43, 655–658 (1991). https://doi.org/10.1007/BF01058555
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DOI: https://doi.org/10.1007/BF01058555