We find an analytic formulation of the notion of Hopf image, in terms of the associated idempotent state. More precisely, if π:A → Mₙ(ℂ) is a finite-dimensional representation of a Hopf C*-algebra, we prove that the idempotent state associated to its Hopf image A' must be the convolution Cesàro limit of the linear functional φ = tr ∘ π. We then discuss some consequences of this result, notably to inner linearity questions.
In this work infinitely divisible cylindrical probability measures on arbitrary Banach spaces are introduced. The class of infinitely divisible cylindrical probability measures is described in terms of their characteristics, a characterisation which is not known in general for infinitely divisible Radon measures on Banach spaces. Further properties of infinitely divisible cylindrical measures such as continuity are derived. Moreover, the classification result enables us to deduce new results on...
On démontre dans cet article des versions probabilistes des injections de Sobolev sur une variété riemannienne compacte, . Plus précisément on démontre que pour des mesures de probabilité naturelles sur l’espace , presque toute fonction appartient à tous les espaces , . On donne ensuite des applications à l’étude des harmoniques sphériques sur la sphère : on démontre (encore pour des mesures de probabilité naturelles) que presque toute base hilbertienne de formée d’harmoniques sphériques...
The heat kernel of a Sturm-Liouville operator with logarithmic potential can be described by using the Wiener integral associated with a real hyperplane arrangement. The heat kernel satisfies an infinite-dimensional analog of the Gauss-Manin connection (integrable system), generalizing a variational formula of Schläfli for the volume of a simplex in the space of constant curvature.
We construct a variant of Koppelman's formula for (0,q)-forms with values in a line bundle, O(l), on projective space. The formula is then applied to a study of a Radon transform for (0,q)-forms, introduced by Gindikin-Henkin-Polyakov. Our presentation follows along the basic lines of Henkin-Polyakov [3], with some simplifications.
Diamo condizioni sulle funzioni , e sulla misura affinché il funzionale sia -semicontinuo inferiormente su . Affrontiamo successivamente il problema del rilassamento.