Hopf's theorem on invariant measures for a group of transformations
How smooth is almost every function in a Sobolev space?
We show that almost every function (in the sense of prevalence) in a Sobolev space is multifractal: Its regularity changes from point to point; the sets of points with a given Hölder regularity are fractal sets, and we determine their Hausdorff dimension.
How subadditive are subadditive capacities?
Subadditivity of capacities is defined initially on the compact sets and need not extend to all sets. This paper explores to what extent subadditivity holds. It presents some incidental results that are valid for all subadditive capacities. The main result states that for all hull-additive capacities (a class that contains the strongly subadditive capacities) there is countable subadditivity on a class at least as large as the universally measurable sets (so larger than the analytic sets).
H-regularidad para medidas vectoriales.
Idempotent States and the Inner Linearity Property
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.
Imbedding theorems for spaces of functions of a denumberable number of variables and their applications.
Induced ...-Homomorphisms and a Parametrization of Measurable Sections via Extremal Preimage Measures.
Induced measures on Wallman spaces.
Inégalités isopérimétriques en analyse et probabilités
Infinitely divisible cylindrical measures on Banach spaces
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...
Injections de Sobolev probabilistes et applications
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...
Integrability for the Dobrakov integral
Integrable cylinder functionals for an integral of Feynman-type
Integrable system of the heat kernel associated with logarithmic potentials
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.
Integral extension with locally-integral seminorm
Integral formulas on projective space and the radon transform of Gindikin-Henkin-Polyakov.
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.
Integral Representation in the Set of Solutions of a Generalized Moment Problem.
Integral representation of measures associated with a foliation
Integral representations of non-linear functionals
Integral transforms, convolution products, and first variations.