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

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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.
Keywords
GENERALIZED-FUNCTIONS, EQUATIONS, TOPOLOGICAL (C)OVER-TILDE-MODULES, COLOMBEAU ALGEBRAS, COEFFICIENTS

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Citation

Please use this url to cite or link to this publication:

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.
@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},
}

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