On absolute summability of Fourier integrals with multipliers

L.G. Bojtsun (Dnipropetrovsk State University)
A.I. Khaliuzova (Dnipropetrovsk State University)

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 $$$f(t) \in L_{(-\infty, \infty)}$$$.

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, 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
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