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Scattering length and capacity

M. Kac, J. M. Luttinger (1975)

Annales de l'institut Fourier

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.

Schwache Konvergenz kanonischer zufälliger Funktionale.

Ulrich Oppel (1973)

Manuscripta mathematica

Sections in function spaces

Henry Helson (1979)

Bulletin de la Société Mathématique de France

Semigroup-theoretical proofs of the central limit theorem and other theorems of analysis.

J. Goldstein (1976)

Semigroup forum

Separabilità di $L^{2}(\mu)$ per spazi riflessivi, $\mu$ misura gaussiana

Adriana Brogini Bratti (1984)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Following H. Sato - Y. Okazaky we will prove that: if $X$ is a topological vector space, locally convex and reflexive, and $\mu$ is a gaussian measure on $\mathbf{C}(X,X^{\prime})$ , then $L^{2}(\mu)$ is separable.

Some basic relationships among transforms, convolution products, first variations and inverse transforms

Seung Chang, Hyun Chung, David Skoug (2013)

Open Mathematics

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.

Some Fine Properties of BV Functions on Wiener Spaces

Luigi Ambrosio, Michele Miranda Jr., Diego Pallara (2015)

Analysis and Geometry in Metric Spaces

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.

Some fine properties of sets with finite perimeter in Wiener spaces

Michele Miranda Jr. (2014)

Banach Center Publications

In this paper we give a brief overview on the state of art of developments of Geometric Measure Theory in infinite-dimensional Banach spaces. The framework is given by an abstract Wiener space, that is a separable Banach space endowed with a centered Gaussian measure. The focus of the paper is on the theory of sets with finite perimeter and on their properties; this choice was motivated by the fact that most of the good properties of functions of bounded variation can be obtained, thanks to coarea...

Some functionals on sets of stationary codes

Štefan Šujan (1985)

Kybernetika

Stabile Maße auf Badrikianschen Räumen.

Egbert Dettweiler (1976)

Mathematische Zeitschrift

Stochastic Basis in Fréchet Space.

Yoshiaki Okazaki (1986)

Mathematische Annalen

Stochastic integration of functions with values in a Banach space

J. M. A. M. van Neerven, L. Weis (2005)

Studia Mathematica

Let H be a separable real Hilbert space and let E be a real Banach space. In this paper we construct a stochastic integral for certain operator-valued functions Φ: (0,T) → ℒ(H,E) with respect to a cylindrical Wiener process ${W_{H} (t)}_{t \in [0, T]}$ . The construction of the integral is given by a series expansion in terms of the stochastic integrals for certain E-valued functions. As a substitute for the Itô isometry we show that the square expectation of the integral equals the radonifying norm of an operator which is...

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