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Abstract
Integral transform, such as Fourier and Mellin are helpful in providing techniques for solving problems in differential equations. It can be used as a mathematical tool to solve these problems. In this paper, we find the correlation of Fourier transform and Mellin transforms of some function and characterizing condition in terms of Mellin transform. This will not only be helpful in solving various differential and integral equations, but also have versatile applications in many fields of applied science.
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References
Andrews, L. C., and B. K. Shivamoggi. Integral Transforms for Engineersand Applied
Mathematicians. New York: Macmillan Publishing, 1988.
Arveson, William. A Short Course on Spectral Theory. New York: Springer,2002.
Batemen, Harry. Tables of Integral Transforms, Vol. I. New York: McGraw-Hill, 1954.
Bauer, Heinz. Probability Theory. Berlin: Walter de Gruyter, 1996.
Butzer, Paul L., and Stefan Jansche. “A direct approach to the Mellin trans-form”. The Journal of
Fourier Analysis and Applications 3 (1997), pp. 325–376.
Hardy G, H, Titchmarsh E. C, A class of Fourier kernels, Proc. London Math. Soc., 35 (1933), 116-
Davis, Harry F. Fourier Series and Orthogonal Functions. New York: DoverPublications, 1989.
Dym, H., and H. P. McKean. Fourier Series and Integrals. New York: Aca-demic Press, 1972. 9. Epstein, Benjamin. “Some applications of the Mellin transform in statistics”.The Annals of
Mathematical Statistics 19 (1948), pp. 370–379.
Flajolet, Philippe, et al. “Mellin transforms and asymptotics: Harmonicsums”. Theoretical Computer
Science 144 (1995), pp. 2-58.
Giffin, Walter C. Transform Techniques for Probability Modeling. NewYork: Academic Press, 1975.
Goffman, Casper, and George Pedrick. First Course in Functional Analysis.Englewood Cliffs, NJ:
Prentice-Hall, 1965.
Hubbard, Barbara Burke. The World According to Wavelets, 2nd Edition.Natick, MA: A K Peters,
Rudin, Walter. Fourier analysis on Groups. New York: Wiley-Interscience,1962.
Watson G. N, General transforms, Proc. London Math. Soc., 35 (1933), 156-99
Springer, M. D., and W. E. Thompson. “The distribution of products ofindependent random
variables”. SIAM Journal on Applied Mathematics 14(1966), pp. 511–526.
Szpankowski,Wojciech. Average Case Analysis of Algorithms on Sequences.New York: Wiley-
Interscience, 2001.
University of St. Andrews. “Robert Hjalmar Mellin” (biography).http://www-history.mcs.standrews.
ac.uk/Biographies/Mellin.html.
Wolf, Kurt B. Integral Transforms in Science and Engineering. New York:Plenum Press, 1979.
Zemanian, A. H. Generalized Integral Transforms. New York: Interscience,1968.