Related papers: Time inhomogeneous Generalized Mehler Semigroups
Let $(G,\theta)$ be a Banach--Lie group with involutive automorphism $\theta$, $\g = \fh \oplus \fq$ be the $\theta$-eigenspaces in the Lie algebra $\g$ of $G$, and $H = (G^\theta)_0$ be the identity component of its group of fixed points.…
Let $\{T(t)\}_{t\geq0}$ be a $C_0$-semigroup on an infinite dimensional separable Hilbert space; a suitable definition of near $\{T(t)^*\}_{t\geq0}$ invariance of a subspace is presented in this paper. A series of prototypical examples for…
We investigate the quantitative stability of the nonlocal Sobolev inequality in Heisenberg group \begin{equation*}\label{non-Sobolev} C_{HL}(Q,\mu)…
This paper deals with collisionless transport equations in bounded open domains $\Omega \subset \R^{d}$ $(d\geq 2)$ with $\mathcal{C}^{1}$ boundary $\partial \Omega $, orthogonally invariant velocity measure $\bm{m}(\d v)$ with support…
We introduce the notion of Bartlett spectral measure for isometrically invariant random measures on proper metric commutative spaces. When the underlying Gelfand pair corresponds to a higher-rank, connected, simple matrix Lie group with…
Initially motivated by Hrushovski's paper on definability patterns, we obtain homeomorphisms between Ellis semigroups related to natural actions of the automorphism groups of first order structures and certain collections of types and…
The theory of dynamical frames evolved from practical problems in dynamical sampling where the initial state of a vector needs to be recovered from the space-time samples of evolutions of the vector. This leads to the investigation of…
In this paper, the dimension-free Harnack inequality is proved for the associated transition semigroups to a large class of stochastic evolution equations with monotone drifts. As applications, the ergodicity, hyper-(or ultra-)contractivity…
We initiate a systematic study of the convolution operation on Keisler measures, generalizing the work of Newelski in the case of types. Adapting results of Glicksberg, we show that the supports of generically stable (or just definable,…
We extend some classical results of Cowling and Meda to the noncommutative setting. Let $(T_t)_{t>0}$ be a symmetric contraction semigroup on a noncommutative space $L_p(\mathcal{M}),$ and let the functions $\phi$ and $\psi$ be regularly…
In 1959, P. Hall introduced the locally finite group $\mathcal{U}$, today known as Hall's universal group. This group is countable, universal, simple, and any two finite isomorphic subgroups are conjugate in $\mathcal{U}$. It can be…
Let G be a semisimple linear algebraic group defined over rational numbers, K be a maximal compact subgroup of its real points and {\Gamma} be an arithmetic lattice. One can associate a probability measure {\mu}(H) on {\Gamma}\G for each…
Time homogeneous polynomial processes are Markov processes whose moments can be calculated easily through matrix exponentials. In this work, we develop a notion of time inhomogeneous polynomial processes where the coeffiecients of the…
A complexified Heisenberg matrix group $\mathrm{H}_\mathbb{C}$ with entries from an infinite-dimensional Hilbert space $H$ is investigated. The Weyl--Schr\"odinger type irreducible representations of $\mathrm{H}_\mathbb{C}$ on the space…
We describe a special class of representations of an inverse semigroup S on Hilbert's space which we term "tight". These representations are supported on a subset of the spectrum of the idempotent semilattice of S, called the "tight…
In this paper we describe the Euler semigroup $\{e^{-t\mathbb{E}^{*}\mathbb{E}}\}_{t>0}$ on homogeneous Lie groups, which allows us to obtain various types of the Hardy-Sobolev and Gagliardo-Nirenberg type inequalities for the Euler…
In this note we introduce the concept of a semi-bounded unitary representations of an infinite-dimensional Lie group $G$. Semi-boundedness is defined in terms of the corresponding momentum set in the dual $\g'$ of the Lie algebra $\g$ of…
We study idempotent measures and the structure of the convolution semigroups of measures over definable groups. We isolate the property of generic transitivity and demonstrate that it is sufficient (and necessary) to develop stable group…
We investigate convergence properties of discrete-time semigroup quantum dynamics, including asymptotic stability, probability and speed of convergence to pure states and subspaces. These properties are of interest in both the analysis of…
Under the Ornstein-Uhlenbeck semigroup $\{U_t\}$, any non-negative measurable $f : \mathbb R^n \to \mathbb R_+$ exhibits a uniform tail bound better than that implied by Markov's inequality and conservation of mass: For every $\alpha \geq…