This paper is about the structure of all entrance laws (in the sense of Dynkin) for time-inhomogeneous Ornstein-Uhlenbeck processes with Lévy noise in Hilbert state spaces. We identify the extremal entrance laws with finite weak first moments through an explicit formula for their Fourier transforms, generalising corresponding results by Dynkin for Wiener noise and nuclear state spaces. We then ...

Doubly stochastic measures are Borel probability measures on the unit square which push forward via the canonical projections to Lebesgue measure on each axis. The set of doubly stochastic measures is convex, so its extreme points are of particular interest. I review necessary and sufficient conditions for a set to support an extremal doubly stochastic measure, and include a proof that such a s...

We give a general inequality for Bergman kernels of spaces defined by convex weights in $\C^n$. also discuss how this can be used Nazarov's proof the Bourgain-Milman theorem, as substitute H\"ormander's estimates $\dbar$-equation.

In 1980 D. Amir and V. D. Milman gave a quantitative finitedimensional version of Krivine’s theorem. We extend their version of the Krivine’s theorem to the quasi-convex setting and provide a quantitative version for p-convex norms. Recently, a number of results of the Local Theory have been extended to the quasi-normed spaces. There are several works [Kal1, Kal2, D, GL, KT, GK, BBP1, BBP2, M2]...

Let V be a finite set andM a finite collection of subsets of V . ThenM is an alignment of V if and only if M is closed under taking intersections and contains both V and the empty set. If M is an alignment of V , then the elements of M are called convex sets and the pair (V,M) is called an aligned space or a convexity space. If S ⊆ V , then the convex hull of S, denoted by CH(S), is the smalles...

In a series of papers, we have shown that from the representation theory of a compact groupoid one can reconstruct the groupoid using the procedure similar to the Tannaka-Krein duality for compact groups. In this part we study continuous representations of compact groupoids. We show that irreducible representationshave finite dimensional fibres. We prove the Schur’s lemma, Gelfand-Raikov theore...