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Title: Hilbert ℂ̃-modules: structural properties and applications to variational problems
Authors: Garetto, Claudia
Vernaeve, Hans
Keywords: Generalized functions
Topological C-modules
Colombeau algebras
Coefficients
Equations
Issue Date: 2011
Publisher: © American Mathematical Society
Citation: GARETTO, C. and VERNAEVE, H., 2011. Hilbert ℂ̃-modules: structural properties and applications to variational problems. Transactions of the American Mathematical Society, 363 (4), pp. 2047-2090.
Abstract: We develop a theory of Hilbert ℂ̃-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 ℂ̃-linear functionals and ℂ̃-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.
Description: First published in Transactions of the American Mathematical Society in 2011, published by the American Mathematical Society
Version: Published
DOI: 10.1090/S0002-9947-2010-05143-8
URI: https://dspace.lboro.ac.uk/2134/15331
Publisher Link: http://dx.doi.org/10.1090/S0002-9947-2010-05143-8
ISSN: 0002-9947
Appears in Collections:Published Articles (Maths)

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