Painlevé’s theorem extended

Claudio Meneghini

Displaying similar documents to “Painlevé’s theorem extended”

The class of holomorphic functions representable by Carleman formula

Lev Aizenberg, Alexander Tumanov, Alekos Vidras (1998)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Integral representation of solutions of first-order linear partial differential equations, I

François Treves (1976)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Holomorphic perturbation of a system of micro-differential equations

Takahiro Kawai (1978)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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A remark on Hartogs' double series

Jaroslav Fuka (1983)

Banach Center Publications

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Formulas for approximate solutions of the ∂∂`-equation in a strictly pseudoconvex domain.

Mats Andersson, Hasse Carlsson (1995)

Revista Matemática Iberoamericana

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Let D be a bounded strictly pseudoconvex domain in C. We construct approximative solution formulas for the equation i∂∂`u = θ, θ being an exact (1,1)-form in D. We show that our formulas give simple proofs of known estimates and indicate further applications.

Analytic continuation of fundamental solutions to differential equations with constant coefficients

Christer O. Kiselman (2011)

Annales de la faculté des sciences de Toulouse Mathématiques

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If $P$ is a polynomial in $R^{n}$ such that $1 / P$ integrable, then the inverse Fourier transform of $1 / P$ is a fundamental solution $E_{P}$ to the differential operator $P (D)$ . The purpose of the article is to study the dependence of this fundamental solution on the polynomial $P$ . For $n = 1$ it is shown that $E_{P}$ can be analytically continued to a Riemann space over the set of all polynomials of the same degree as $P$ . The singularities of this extension are studied.

Strong boundary values : independence of the defining function and spaces of test functions

Jean-Pierre Rosay, Edgar Lee Stout (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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The notion of “strong boundary values” was introduced by the authors in the local theory of hyperfunction boundary values (boundary values of functions with unrestricted growth, not necessarily solutions of a PDE). In this paper two points are clarified, at least in the global setting (compact boundaries): independence with respect to the defining function that defines the boundary, and the spaces of test functions to be used. The proofs rely crucially on simple results in spectral asymptotics. ...