This paper is about the structure of all entrance laws (in sense Dynkin) for time-inhomogeneous Ornstein–Uhlenbeck processes with Lévy noise in Hilbert state spaces. We identify extremal finite weak first moments through an explicit formula their Fourier transforms, generalizing corresponding results by Dynkin Wiener and nuclear then prove that arbitrary law can be uniquely represented as integ...

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.

This article investigates the notions of exposed points and (exposed) faces in matrix convex setting. Matrix finite dimensions were first defined by Kriel 2019. Here this notion is extended to sets infinite-dimensional vector spaces. Then a connection between extreme established: point ordinary if only it exposed. leads Krein-Milman type result for that due Straszewicz-Klee classical convexity:...

We introduce a new approach to Nehari’s problem. This approach is based on some kind of fixed point theorem and allows us to obtain some useful generalizations of Nehari’s and Adamyan – Arov – Krein (AAK) theorems. Among those generalizations: descriptions of Hankel operators in weighted 2 spaces; descriptions of Hankel operators from Dirichlet type spaces to weighted Bergman spaces; commutant ...