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

Christian Brouder, Nguyen Viet Dang, and Frédéric Hélein. "Continuity of the fundamental operations on distributions having a specified wave front set (with a counterexample by Semyon Alesker)." Studia Mathematica 232.3 (2016): 201-226. <http://eudml.org/doc/285412>.

@article{ChristianBrouder2016,
abstract = {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 $^\{\prime \}_\{Γ\}$ 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 $^\{\prime \}_\{Γ\}$, 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.},
author = {Christian Brouder, Nguyen Viet Dang, Frédéric Hélein},
journal = {Studia Mathematica},
keywords = {microlocal analysis; functional analysis; mathematical physics; renormalization},
language = {eng},
number = {3},
pages = {201-226},
title = {Continuity of the fundamental operations on distributions having a specified wave front set (with a counterexample by Semyon Alesker)},
url = {http://eudml.org/doc/285412},
volume = {232},
year = {2016},
}

TY - JOUR
AU - Christian Brouder
AU - Nguyen Viet Dang
AU - Frédéric Hélein
TI - Continuity of the fundamental operations on distributions having a specified wave front set (with a counterexample by Semyon Alesker)
JO - Studia Mathematica
PY - 2016
VL - 232
IS - 3
SP - 201
EP - 226
AB - 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 $^{\prime }_{Γ}$ 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 $^{\prime }_{Γ}$, 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.
LA - eng
KW - microlocal analysis; functional analysis; mathematical physics; renormalization
UR - http://eudml.org/doc/285412
ER -