Displaying similar documents to “Uniqueness and regularity properties of linear operators and their applications”

Asymptotic solutions to Fuchsian equations in several variables

Boris Sternin, Victor Shatalov (1996)

Banach Center Publications

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The aim of this paper is to construct asymptotic solutions to multidimensional Fuchsian equations near points of their degeneracy. Such construction is based on the theory of resurgent functions of several complex variables worked out by the authors in [1]. This theory allows us to construct explicit resurgent solutions to Fuchsian equations and also to investigate evolution equations (Cauchy problems) with operators of Fuchsian type in their right-hand parts.

Laurent series expansion for solutions of hypoelliptic equations

M. Langenbruch (2002)

Annales Polonici Mathematici

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We prove that any zero solution of a hypoelliptic partial differential operator can be expanded in a generalized Laurent series near a point singularity if and only if the operator is semielliptic. Moreover, the coefficients may be calculated by means of a Cauchy integral type formula. In particular, we obtain explicit expansions for the solutions of the heat equation near a point singularity. To prove the necessity of semiellipticity, we additionally assume that the index of hypoellipticity...