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arXiv · 0707.1104

Hilbert $\widetilde{\C}$-modules: structural properties and applications to variational problems

Claudia Garetto·Hans Vernaeve
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Abstract

We develop a theory of Hilbert $\widetilde{\C}$-modules by investigating their structural and functional analytic properties. Particular attention is given to finitely generated submodules, projection operators, representation theorems for $\widetilde{\C}$-linear functionals and $\widetilde{\C}$-sesquilinear forms. By making use of a generalized Lax-Milgram theorem, we provide some existence and uniqueness theorems for variational problems involving a generalized bilinear or sesquilinear form.

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BibTeXRIS

Claudia Garetto, Hans Vernaeve. 2007-07-07. Hilbert $\widetilde{\C}$-modules: structural properties and applications to variational problems. https://arxiv.org/abs/0707.1104

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