Theoretical solution for a direct problem in thin layer elastic medium in spectral domain can be obtained using Laplace and Fourier-Bessel transforms. In practice it is important to know properties of the discrete transforms and their influence on the resulting solutions. We present results of investigations of these properties using explicitly defined functions. This approach allows to analyze some important properties of the transforms. In this study we identify conditions under which these transforms can be applied. It is illustrated in a number of specific examples.

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