In this research, we investigate the spectral expansions connected with elliptic differential operators in the space of singular distributions, which describes the vibration process made of thin elastic membrane stretched tightly over a circular frame. The sufficient conditions for summability of the spectral expansions connected with wave problems on the disk are obtained by taking into account that the deflection of the membrane during the motion remains small compared to the size of the membrane and for wave propagation problems, the disk is made of some thermally conductive material.
In this paper, we deal with the problems of the expansions of the periodic distributions. We obtained sufficient conditions for the equiconvergence of the spectral decompositions of the distributions connected with the elliptic differential operator on the torus with Fourier integral in the classes of the Sobolev.
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