Abstract:
We characterize the closed ideals in some algebras of analytic functions, the algebra of absolutely convergent Taylor series and in analytic weighted Lipschitz algebras. The Hodge de Rham decomposition for anL^2 space of differential two-forms and vanishing of L^2 harmonic one-forms on path spaces are considered. We show the vanishing theorem of the Hodge-Kodaira operator and the generalized Clarc-Ocone formulae for differential forms. Some applications of Krien’s theory of regular symmetric operators to sampling and analytic sampling theory in a Hilbert space are investigated.
