Hilbert $\widetilde{\mathbb{C}}$-modules: Structural properties and applications to variational problems
Hilbert $\widetilde{\mathbb{C}}$-modules: Structural properties and applications to variational problems
We develop a theory of Hilbert $\widetilde {\mathbb {C}}$-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 $\widetilde {\mathbb {C}}$-linear functionals and $\widetilde {\mathbb {C}}$-sesquilinear forms. We establish a generalized …