# Schwartz kernel theorem in algebras of generalized functions

Banach Center Publications (2010)

- Volume: 88, Issue: 1, page 285-296
- ISSN: 0137-6934

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topVincent 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 -

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