Abstract
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.
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