International Journal of Partial Differential Equations and Applications
ISSN (Print): 2376-9548 ISSN (Online): 2376-9556 Website: Editor-in-chief: Mahammad Nurmammadov
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International Journal of Partial Differential Equations and Applications. 2014, 2(5), 91-95
DOI: 10.12691/ijpdea-2-5-2
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Matrix Fourier Transforms and Application

O. Yaremko1, O. Nikitina1 and E. Zuravleva1,

1Oleg Yaremko,Olga Nikitina, Ekaterina Zuravleva Penza State University, Penza, Russia

Pub. Date: November 18, 2014

Cite this paper:
O. Yaremko, O. Nikitina and E. Zuravleva. Matrix Fourier Transforms and Application. International Journal of Partial Differential Equations and Applications. 2014; 2(5):91-95. doi: 10.12691/ijpdea-2-5-2


In this work, we introduce in an explicit form a special types of matrix Fourier transforms on real axis and real semi- axis: matrix cos- transforms, matrix sin- transforms and matrix transforms with piecewise trigonometric kernels. The integral transforms of such kinds are used for solving analytically the problems of mathematical physics in homogeneous and piecewise homogeneous media. Analytical solution of vector heat conduction equation,vector wave equation and vector Poisson equation is obtained.

fourier matrix transforms integral transform heat conduction equation wave equation Poisson equation

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[1]  Uflyand I. S. (1967) Integral transforms in the problem of the theory of elasticity. Leningrad. Science, p. 402
[2]  Uflyand I. S. (1967) On some new integral transformations and their applications to problems of mathematical physics. Problems of mathematical physics. Leningrad, p. 93-106
[3]  M.P.Lenjuk, Integral'noe preobrazovanie Fur'e na kusochno-odnorodnoj poluprjamoj, Izv. vuzov. Matematika, Volume 4,1989, p. 14-18.
[4]  L.S.Najda, Gibridnye integral'nye preobrazovanija tipa Hankelja-Lezhandra, Mat. metody analiza dinam. sistem, Har'kov, Volume 8, 1984, p. 132-135.
[5]  V.S.Procenko, A.I.Solov'jov, Gibridnye integral'nye preobrazovanija i ih prilozhenija v teorii uprugosti neodnorodnyh sred, Prikladnaja mehanika, Issue 1, Volume 13, 1982, p. 62-67.
[6]  E. Mogileva, O. Yaremko, Hermite functions with discontinuous coefficients for the solution of fractal diffusion retrospective problems, International journal of applied mathematics and informatics,Issue 3, Volume 7, 2013, p. 78-86.
[7]  F.M. Mors, G. Fishbah, Methods of theoretical physics, New York, McGraw-Hill, 1953. Part I, 998 pp.
[8]  O.E. Yaremko, Matrix integral Fourier transforms for problems with discontinuous coefficients and transformation operators, Reports of Academy of Sciences, Volume. 417, Issue 3, 2007, p. 323-325.
[9]  Bavrin I.I., Matrosov V.L., Jaremko O. E. (2006) Operators of transformation in the analysis, mathematical physics and Pattern recognition. Moscow, Prometheus, p 292.
[10]  Brejsuell R., (1990) Hartley transform, Moscow, World, p 584.
[11]  Vladimirov V. S., Zharinov V.V., (2004) The equations of mathematical physics, Moscow, Phys mat lit, p 400.
[12]  Gantmaxer F.R., (2010) Theory matrix. Moscow, Phys. Mat. Lit., p 560.
[13]  Sneddon I., (1955) Fourier Transform, Moscow.
[14]  Physical encyclopedia. The editor-in-chief A. M. Prokhorov, D.M. Alekseev, Moscow, (1988-1998).
[15]  Jaremko O. E., (2007) Matrix integral Fourier transform for problems with discontinuous coefficients and conversion operators. Proceedings of the USSR Academy of Sciences. p. 323-325.