Journal
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
Volume 363, Issue 4, Pages 2047-2090Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/S0002-9947-2010-05143-8
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Funding
- FWF (Austria) [T305-N13, Y237-N13, M949-N18]
- Austrian Science Fund (FWF) [Y 237] Funding Source: researchfish
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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 subrnodules, 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.
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