Displaying similar documents to “Classical PLS-spaces: spaces of distributions, real analytic functions and their relatives”

Generalized analytic functions with applications to singular ordinary and partial differential equations

Bogdan Ziemian

Similarity:

CONTENTS Introduction.............................................................................................................................................5 I. Preliminaries.........................................................................................................................................7    1. A review of classical results in the theory of Laplace integra............................................................7    2. Boundary values of holomorphic functions......................................................................................10...

Characterization of surjective partial differential operators on spaces of real analytic functions

Michael Langenbruch (2004)

Studia Mathematica

Similarity:

Let A(Ω) denote the real analytic functions defined on an open set Ω ⊂ ℝⁿ. We show that a partial differential operator P(D) with constant coefficients is surjective on A(Ω) if and only if for any relatively compact open ω ⊂ Ω, P(D) admits (shifted) hyperfunction elementary solutions on Ω which are real analytic on ω (and if the equation P(D)f = g, g ∈ A(Ω), may be solved on ω). The latter condition is redundant if the elementary solutions are defined on conv(Ω). This extends and improves...

A note on composition operators on spaces of real analytic functions

Paweł Domański, Michał Goliński, Michael Langenbruch (2012)

Annales Polonici Mathematici

Similarity:

We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semiproper map φ such that the associated composition operator is not open onto its image.