Schwartz kernel theorem in algebras of generalized functions

Vincent Valmorin. "Schwartz kernel theorem in algebras of generalized functions." Banach Center Publications 88.1 (2010): 285-296. <http://eudml.org/doc/281819>.

@article{VincentValmorin2010,
abstract = {A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of $G^\{∞\}$-generalized functions class are given. A straightforward relationship between the classical and the generalized versions of Schwartz’s kernel theorem is established.},
author = {Vincent Valmorin},
journal = {Banach Center Publications},
keywords = {Schwartz's kernel theorem; Colombeau algebras},
language = {eng},
number = {1},
pages = {285-296},
title = {Schwartz kernel theorem in algebras of generalized functions},
url = {http://eudml.org/doc/281819},
volume = {88},
year = {2010},
}

TY - JOUR
AU - Vincent Valmorin
TI - Schwartz kernel theorem in algebras of generalized functions
JO - Banach Center Publications
PY - 2010
VL - 88
IS - 1
SP - 285
EP - 296
AB - A new approach to the generalization of Schwartz’s kernel theorem to Colombeau algebras of generalized functions is given. It is based on linear maps from algebras of classical functions to algebras of generalized ones. In particular, this approach enables one to give a meaning to certain hypotheses in preceding similar work on this theorem. Results based on the properties of $G^{∞}$-generalized functions class are given. A straightforward relationship between the classical and the generalized versions of Schwartz’s kernel theorem is established.
LA - eng
KW - Schwartz's kernel theorem; Colombeau algebras
UR - http://eudml.org/doc/281819
ER -