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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...

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 ∈ [ 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...

The symmetric property ( τ ) for the Gaussian measure

Joseph Lehec (2008)

Annales de la faculté des sciences de Toulouse Mathématiques

We give a proof, based on the Poincaré inequality, of the symmetric property ( τ ) for the Gaussian measure. If f : ℝ d → ℝ is continuous, bounded from below and even, we define H f ( x ) = inf y f ( x + y ) + 1 2 | y | 2 and we have ∫ e - f d γ d ∫ e H f d γ d ≤ 1 . This property is equivalent to a certain functional form of the Blaschke-Santaló inequality, as explained in a paper by Artstein, Klartag and Milman.

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