Fundamental solution for the Helmholtz equation
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Abstract
This paper deals with the construction of a family of fundamental solutions of the Helmholtz equation, parameterized by an entire function with certain properties. Functions that possess these properties are called the Carleman function. On the basis of the proved lemmas for the Helmholtz equation in two-dimensional and three-dimensional bounded domains, in what follows we will find a regularized solution of the Cauchy problem already for a multidimensional domain.
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References
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