Absolute summation of Fourier integrals with multiplier by G.F. Voronoi method

L.G. Bojtsun (Oles Honchar Dnipropetrovsk National University)
S.V. Kocherga (Oles Honchar Dnipropetrovsk National University)

Abstract


We provide the theorem that is connected with functional method of G.F. Voronoi. We establish sufficient conditions for a function that generates the summation method of G.F. Voronoi, on function-multiplier, and on function $$$f(t)$$$, under which the Fourier integral of this function with multiplier is absolutely summable by the functional method of G.F. Voronoi.

References


Voronoi G.F. Extension of concept of infinite series sum limit. In: Sobr. soch. in 3 vol., Kyiv, 1952; 3: pp. 9-10. (in Russian)

Titchmarsh E.C. Introduction to the theory of Fourier integral, Moscow, 1948; 479 p. (in Russian)


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Copyright (c) 2008 L.G. Bojtsun, S.V. Kocherga

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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
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