Abstract
We introduce an integral transform related to a Fourier sine-Fourier - Fourier cosine generalized convolution and prove a Watson type theorem for the transform. As applications we obtain solutions of some integral equations in closed form.
Similar content being viewed by others
References
F. Al-Musallam, V.K. Tuan, Integral transforms related to a generalized convolution. Results Math. 38, No 3–4 (2000), 197–208.
H. Bateman, A. Erdélyi, Tables of Integral Transforms, Vol. I. McGraw-Hill Book Co., New York-Toronto-London (1954).
L.E. Britvina, A class of integral transforms related to the Fourier cosine convolution. Integr. Trans. Spec. Func., 16, No 5–6 (2005), 379–389.
J. Duoadikoetxea, Fourier Analysis. AMS, Providence, Rhode Island (2001).
I.S. Gradshteyn, I.M. Ryzhik, Tables of Integrals, Series, and Products, 7ed. Academic Press (2007).
Y.N. Grigoriev, N.H. Ibragimov, V.F. Kovalev, S.V. Meleshko, Symmetries of Integro-Differential Equations with Applications in Mechanics and Plasma Physics. Lect. Notes Phys. 806, Springer, Dordrecht (2010).
V.A. Kakichev, N.X. Thao, On the design method for the generalized integral convolutions. Izv. Vyssh. Uchebn. Zaved. Mat., No 1 (1998), 31–40 (In Russian).
V.A. Kakichev, N.X. Thao, V.K. Tuan, On the generalized convolutions for Fourier cosine and sine transforms. East-West J. of Math., 1, No 1 (1998), 85–90.
N.M. Khoa, On the generalized convolution with a weight function for Fourier cosine, Fourier and Fourier sine transforms. Southeast Asian Bull. Math., 33 (2009), 285–298.
R.E.A.C. Paley, N. Wiener, Fourier Transforms in the Complex Domain. AMS, New York (1934).
I.N. Sneddon, Fourier Transforms. McGray-Hill, New York (1951).
E.C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 3ed. Chelsea Publishing Co., New York (1986).
V.K. Tuan, Integral transforms of Fourier cosine convolution type. J. Math. Anal. Appl. 229, No 2 (1999), 519–529.
N.X. Thao, N.M. Khoa, On the generalized convolution for Fourier sine, Fourier and Fourier cosine transforms. In: Proc. Function Spaces in Complex and Clifford Analysis, National University Publisher, Hanoi (2008), 223–240.
Author information
Authors and Affiliations
Corresponding author
About this article
Cite this article
Thao, N.X., Tuan, V.K. & Hong, N.T. A Fourier generalized convolution transform and applications to integral equations. fcaa 15, 493–508 (2012). https://doi.org/10.2478/s13540-012-0035-y
Received:
Published:
Issue Date:
DOI: https://doi.org/10.2478/s13540-012-0035-y