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., Kyiv, 1952; 3: pp. 9-10. (in Russian)
Titchmarsh E.C. Introduction to the theory of Fourier integral, Gostekhizdat, 1948. (in Russian)
Bojtsun L.G. "On absolute summability of conjugate Fourier integrals by method of G.F. Voronoi", Izv. vuzov. Ser. Matematika, 1967; 6: pp. 11-21. (in Russian)
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
