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Hilbert C-modules: structural properties and applications to variational problems

Claudia Garetto and Hans Vernaeve UGent (2011) TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 363(4). p.2047-2090
abstract
Abstract.We develop a theory of Hilbert (C)over-tilde-modules which forms the core of a new functional analytic approach to algebras of generalized functions. Particular attention is given to finitely generated submodules, projection operators, representation theorems for (C)over-tilde-linear functionals and (C)over-tilde-sesquilinear forms. We establish a generalized Lax-Milgram theorem and use it to prove existence and uniqueness theorems for variational problems involving a generalized bilinear or sesquilinear form.
Please use this url to cite or link to this publication:
author
organization
alternative title
Hilbert (C)over-tilde-modules : structural properties and applications to variational problems
year
type
journalArticle (original)
publication status
published
subject
keyword
GENERALIZED-FUNCTIONS, EQUATIONS, TOPOLOGICAL (C)OVER-TILDE-MODULES, COLOMBEAU ALGEBRAS, COEFFICIENTS
journal title
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Trans. Am. Math. Soc.
volume
363
issue
4
pages
2047 - 2090
Web of Science type
Article
Web of Science id
000288618200016
JCR category
MATHEMATICS
JCR impact factor
1.093 (2011)
JCR rank
33/288 (2011)
JCR quartile
1 (2011)
ISSN
0002-9947
DOI
10.1090/S0002-9947-2010-05143-8
language
English
UGent publication?
no
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1849932
handle
http://hdl.handle.net/1854/LU-1849932
date created
2011-06-30 15:52:43
date last changed
2016-12-19 15:42:17
@article{1849932,
  abstract     = {Abstract.We develop a theory of Hilbert (C)over-tilde-modules which forms the core of a new functional analytic approach to algebras of generalized functions. Particular attention is given to \unmatched{fb01}nitely generated submodules, projection operators, representation theorems for (C)over-tilde-linear functionals and (C)over-tilde-sesquilinear forms. We establish a generalized Lax-Milgram theorem and use it to prove existence and uniqueness theorems for variational problems involving a generalized bilinear or sesquilinear form.},
  author       = {Garetto, Claudia and Vernaeve, Hans},
  issn         = {0002-9947},
  journal      = {TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY},
  keyword      = {GENERALIZED-FUNCTIONS,EQUATIONS,TOPOLOGICAL (C)OVER-TILDE-MODULES,COLOMBEAU ALGEBRAS,COEFFICIENTS},
  language     = {eng},
  number       = {4},
  pages        = {2047--2090},
  title        = {Hilbert C-modules: structural properties and applications to variational problems},
  url          = {http://dx.doi.org/10.1090/S0002-9947-2010-05143-8},
  volume       = {363},
  year         = {2011},
}

Chicago
Garetto, Claudia, and Hans Vernaeve. 2011. “Hilbert C-modules: Structural Properties and Applications to Variational Problems.” Transactions of the American Mathematical Society 363 (4): 2047–2090.
APA
Garetto, C., & Vernaeve, H. (2011). Hilbert C-modules: structural properties and applications to variational problems. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 363(4), 2047–2090.
Vancouver
1.
Garetto C, Vernaeve H. Hilbert C-modules: structural properties and applications to variational problems. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. 2011;363(4):2047–90.
MLA
Garetto, Claudia, and Hans Vernaeve. “Hilbert C-modules: Structural Properties and Applications to Variational Problems.” TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 363.4 (2011): 2047–2090. Print.