Continuity of the fundamental operations on distributions having a specified wave front set (with a counterexample by Semyon Alesker)

• Autorzy: Christian Brouder , Nguyen Viet Dang , Frédéric Hélein
• Języki publikacji: EN

Abstrakty

EN

The pull-back, push-forward and multiplication of smooth functions can be extended to distributions if their wave front sets satisfy some conditions. Thus, it is natural to investigate the topological properties of these operations between spaces $𝓓'_{Γ}$ of distributions having a wave front set included in a given closed cone Γ of the cotangent space. As discovered by S. Alesker, the pull-back is not continuous for the usual topology on $𝓓'_{Γ}$, and the tensor product is not separately continuous. In this paper, a new topology is defined for which the pull-back and push-forward are continuous, and the tensor and convolution products and multiplication of distributions are hypocontinuous.

Kategorie tematyczne

• 35A18: Wave front sets
• 46F10: Operations with distributions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2016
• Tom: 232
• Numer: 3
• Strony: 201-226

Daty

wydano

2016

Twórcy

autor

Christian Brouder

• Sorbonne Universités, UPMC Univ. Paris 06, CNRS UMR 7590
• Muséum National d'Histoire Naturelle, IRD UMR 206

autor

Nguyen Viet Dang

• Institut Camille Jordan, Université Claude Bernard Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France

autor

Frédéric Hélein

• Institut de Mathématiques de Jussieu Paris Rive Gauche, Université Denis Diderot Paris 7, Bâtiment Sophie Germain, 75205 Paris Cedex 13, France

Identyfikatory

DOI

10.4064/sm8316-3-2016