Scattering length and capacity
An expression in terms of the Wiener integral for the “scattering length” is given and used to discuss the relation between this quantity and electrostatic capacity.
An expression in terms of the Wiener integral for the “scattering length” is given and used to discuss the relation between this quantity and electrostatic capacity.
Following H. Sato - Y. Okazaky we will prove that: if is a topological vector space, locally convex and reflexive, and is a gaussian measure on , then is separable.
We extend some known sigma-finiteness and regularity results for (locally finite) Radon measures to locally sigma-finite or locally moderated Radon measures of type (H), and we obtain other new ones. The main result states that the regularity and the sigma-finiteness are equivalent for alllocally moderated, diffused, Radon measures of type (H) in a T1 topological space which is either weakly metacompact or paralindelöf (resp. metalindelöf) and has a concassage of Lindelöf (resp. separable) subsets....
In this paper we obtain several basic formulas for generalized integral transforms, convolution products, first variations and inverse integral transforms of functionals defined on function space.
In this paper we define jump set and approximate limits for BV functions on Wiener spaces and show that the weak gradient admits a decomposition similar to the finite dimensional case. We also define the SBV class of functions of special bounded variation and give a characterisation of SBV via a chain rule and a closure theorem. We also provide a characterisation of BV functions in terms of the short-time behaviour of the Ornstein-Uhlenbeck semigroup following an approach due to Ledoux.