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

journal contribution
posted on 25.07.2014 by Claudia Garetto, Hans Vernaeve
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.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Transactions of the American Mathematical Society

Volume

363

Issue

4

Pages

2047 - 2090

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.

Publisher

© American Mathematical Society

Version

VoR (Version of Record)

Publication date

2011

Notes

First published in Transactions of the American Mathematical Society in 2011, published by the American Mathematical Society

ISSN

0002-9947

eISSN

1088-6850

Language

en

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