On absolute summability of Fourier integrals with multipliers
Abstract
We obtain the conditions for function that generates functional method and for the multiplier $$$\mu(y)$$$ that are sufficient for absolute summability of
$$\int\limits_0^{\infty} \mu (y) B(y, t) dy$$
where $$$\int\limits_0^{\infty} B(y, t) dy$$$ is the Fourier integral of a function $$$f(t) \in L_{(-\infty, \infty)}$$$.
$$\int\limits_0^{\infty} \mu (y) B(y, t) dy$$
where $$$\int\limits_0^{\infty} B(y, t) dy$$$ is the Fourier integral of a function $$$f(t) \in L_{(-\infty, \infty)}$$$.
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Voronoi G.F. Extension of concept of infinite series sum limit. In: Sobr. soch. in 3 vol., 1952; 3: pp. 9-10.
Titchmarsh E.C. Introduction to the theory of Fourier integral, Gostekhizdat, 1948.
Bojtsun L.G. "On absolute summability of conjugate Fourier integrals by method of G.F. Voronoi", Izv. VUZov. Matem., 1967; 6: pp. 11-21.
DOI: https://doi.org/10.15421/248713
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Copyright (c) 1987 L.G. Bojtsun, A.I. Khaliuzova
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ISSN (Online): 2664-5009
ISSN (Print): 2664-4991
