Analysis on Wiener spaces. II. Differential forms

Differential Forms on Noncommutative Spaces

This paper is intended as an introduction to noncommutative geometry for readers with some knowledge of abstract algebra and differential geometry. We show how to extend the theory of differential forms to the “noncommutative spaces” studied in noncommutative geometry. We formulate and prove the Hochschild-Kostant-Rosenberg theorem and an extension of this result involving the Connes differential.

LOGARITHMIC DIFFERENTIAL FORMS ON p-ADIC SYMMETRIC SPACES

We give an explicit description in terms of logarithmic differential forms of the isomorphism of P. Schneider and U. Stuhler relating de Rham cohomology of p-adic symmetric spaces to boundary distributions. As an application we prove a Hodgetype decomposition for the de Rham cohomology of varieties over p-adic fields which admit a uniformization by a p-adic symmetric space.

An Infinitesimal Approach to Stochastic Analysis on Abstract Wiener Spaces

Differential forms on locally convex spaces and the Stokes formula

We prove a version of the Stokes formula for differential forms on locally convex spaces announced in [10]. The main tool used for proving this formula is the surface layer theorem proved in the paper [6] by the author. Moreover, for differential forms of a Sobolev-type class relative to a differentiable measure [1], we compute the operator adjoint to the exterior differential in terms of stand...

On high order finite element spaces of differential forms

We show how the high order finite element spaces of differential forms due to Raviart-Thomas-Nédelec-Hiptmair fit into the framework of finite element systems, in an elaboration of the finite element exterior calculus of Arnold-Falk-Winther. Based on observations by Bossavit, we provide new low order degrees of freedom. As an alternative to existing choices of bases, we provide canonical resolu...