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On splitting up singularities of fundamental solutions to elliptic equations in \(\mathbb C^{2}\). (English) Zbl 1145.35308
Summary: It is known that the fundamental solution to an elliptic differential equation with analytic coefficients exists, is determined up to the kernel of the differential operator, and has singularities on characteristics of the equation in \(\mathbb C^{2}\). In this paper we construct a representation of fundamental solution as a sum of functions, each of those has singularity on a single characteristic.

35A20 Analyticity in context of PDEs
35A08 Fundamental solutions to PDEs
32S70 Other operations on complex singularities
35J15 Second-order elliptic equations
32W50 Other partial differential equations of complex analysis in several variables
35C15 Integral representations of solutions to PDEs
Full Text: DOI
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