Extension of distributions and representation by derivatives of continuous functions.
- Volume: 7, Issue: 1, page 31-40
- ISSN: 1120-6330
Access Full Article
top
Abstract
topHow to cite
topLemoine, Jérôme, and Simon, Jacques. "Extension of distributions and representation by derivatives of continuous functions.." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 7.1 (1996): 31-40. <http://eudml.org/doc/244168>.
@article{Lemoine1996,
abstract = {It is proved that any Banach valued distribution on a bounded set can be extended to all of \( \mathbb\{R\}^\{d\} \) if and only if it is a derivative of a uniformly continuous function. A similar result is given for distributions on an unbounded set. An example shows that this does not extend to Frechet valued distributions. This relies on the fact that a Banach valued distribution is locally a derivative of a uniformly continuous function. For sake of completeness, a global representation of a Banach valued distribution by derivatives of functions with compact supports is given.},
author = {Lemoine, Jérôme, Simon, Jacques},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Distributions; Extension; Vector-values; Representation; Banach valued distribution on a bounded set; Fréchet valued distributions; global representation of a Banach valued distribution by derivatives of functions with compact supports},
language = {eng},
month = {5},
number = {1},
pages = {31-40},
publisher = {Accademia Nazionale dei Lincei},
title = {Extension of distributions and representation by derivatives of continuous functions.},
url = {http://eudml.org/doc/244168},
volume = {7},
year = {1996},
}
TY - JOUR
AU - Lemoine, Jérôme
AU - Simon, Jacques
TI - Extension of distributions and representation by derivatives of continuous functions.
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1996/5//
PB - Accademia Nazionale dei Lincei
VL - 7
IS - 1
SP - 31
EP - 40
AB - It is proved that any Banach valued distribution on a bounded set can be extended to all of \( \mathbb{R}^{d} \) if and only if it is a derivative of a uniformly continuous function. A similar result is given for distributions on an unbounded set. An example shows that this does not extend to Frechet valued distributions. This relies on the fact that a Banach valued distribution is locally a derivative of a uniformly continuous function. For sake of completeness, a global representation of a Banach valued distribution by derivatives of functions with compact supports is given.
LA - eng
KW - Distributions; Extension; Vector-values; Representation; Banach valued distribution on a bounded set; Fréchet valued distributions; global representation of a Banach valued distribution by derivatives of functions with compact supports
UR - http://eudml.org/doc/244168
ER -
References
top- DUGUNDJI, J., Topology. Allyn and Bacon, Inc., Boston1966. Zbl0397.54003MR193606
- SCHWARTZ, L., Théorie des distributions à valeurs vectorielles. Annales de l'Institut Fourier, tome VII, 1957. Zbl0078.11003
- SCHWARTZ, L., Théorie des distributions. Hermann 1966 (ed. of 1973). Zbl0149.09501MR209834
- SIMON, J., Distributions à valeurs dans un espace séquentiellement complet. Preprint of Laboratoire de Mathématiques Appliquées, Université Blaise Pascal, 1996, to appear.
NotesEmbed ?
topYou must be logged in to post comments.
To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.