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Universal zero solutions of linear partial differential operators

Thomas Kalmes, Markus Niess (2010)

Studia Mathematica

A generalized approach to several universality results is given by replacing holomorphic or harmonic functions by zero solutions of arbitrary linear partial differential operators. Instead of the approximation theorems of Runge and others, we use an approximation theorem of Hörmander.

Various kinds of sensitive singular perturbations

Nicolas Meunier, Jacqueline Sanchez-Hubert, Évariste Sanchez-Palencia (2007)

Annales mathématiques Blaise Pascal

We consider variational problems of P. D. E. depending on a small parameter ε when the limit process ε 0 implies vanishing of the higher order terms. The perturbation problem is said to be sensitive when the energy space of the limit problem is out of the distribution space, so that the limit problem is out of classical theory of P. D. E. We present here a review of the subject, including abstract convergence theorems and two very different model problems (the second one is presented for the first...

When is a Riesz distribution a complex measure?

Alan D. Sokal (2011)

Bulletin de la Société Mathématique de France

Let α be the Riesz distribution on a simple Euclidean Jordan algebra, parametrized by α . I give an elementary proof of the necessary and sufficient condition for α to be a locally finite complex measure (= complex Radon measure).

White noise distribution theory and its application

Yoshihito Shimada (2007)

Banach Center Publications

The paper gives a new application of the white noise distribution theory via a proof of irreducibility of the energy representation of a group of C -maps from a compact Riemann manifold to a semi-simple compact Lie group.

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