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The construction of fundamental solutions in R3 for the equations of harmonic vibrations in the theory of elasticity of anisotropic elastic media is carried out. Solutions are constructed in the form of multipole series. Theorems on the convergence of series in the topology of compact convergence in R3/0 are proved. The problems on constructing some singular solutions of the theory of vibrations of an anisotropic body are discussed. The fundamental solution of the oscillation equations for an isotropic medium is obtained in a closed form.
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A. V. Ilyashenko (2023) studied this question.
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