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Multidimensional integral transformations with non-separated variables forproblems with discontinuous coefficients are constructed in this work. Thecoefficient discontinuities focused on the of parallel hyperplanes. In thiswork explicit formulas for the kernels in the case of ideal coupling conditionsare obtained; the basic identity of the integral transform is proved; techniqueof integral transforms is developed

Solving the heat equation in piecewise-homogeneous anisotropic media using the multidimensional Fourier transforms