Related papers: Time regularity for generalized Mehler semigroups

We establish sharp interior and boundary regularity estimates for solutions to $\partial_t u - L u = f(t, x)$ in $I\times \Omega$, with $I \subset \mathbb{R}$ and $\Omega \subset\mathbb{R}^n$. The operators $L$ we consider are…

We consider a Thomas-Fermi mean-field model for large neutral atoms. That is, Schr\"odinger operators $H_Z^{\text{TF}}=-\Delta-\Phi_Z^{\text{TF}}$ in three-dimensional space, where $Z$ is the nuclear charge of the atom and…

We prove an extension theorem for a small perturbation of the Ornstein-Uhlenbeck operator $(L,D(L))$ in the space of all uniformly continuous and bounded functions $f:H\to \Rset$, where $H$ is a separable Hilbert space. We consider a…

Given a bounded domain in the Euclidean space satisfying the uniform outer cone condition, we show that a uniformly elliptic operator of second order with continuous second order coefficients generates a holomorphic semigroup on the space…

We give several functional inequalities related to the Ornstein-Uhlenbeck semigroup in the Dunkl differential-difference operators setting. As an application of these inequalities, we derive out a Sobolev-logarithmic and an…

We study here the effects of a time-dependent second order perturbation to a degenerate Ornstein-Uhlenbeck type operator whose diffusive part can be either local or non-local. More precisely, we establish that some estimates, such as the…

We study maximal regularity with respect to continuous functions for strongly continuous semigroups on locally convex spaces as well as its relation to the notion of admissible operators. This extends several results for classical strongly…

We characterize the domain of the realization of the linear parabolic operator Gu := u_t + L(t)u (where, for each real t, L(t) is an Ornstein-Uhlenbeck operator), in L^2 spaces with respect to a suitable measure, that is invariant for the…

In this paper we establish a result regarding the connection between continuous maximal regularity and generation of analytic semigroups on a pair of densely embedded Banach spaces. More precisely, we show that continuous maximal regularity…

We give a new more explicit proof of a result by Kalton & Lancien stating that on each Banach space with an unconditional basis not isomorphic to a Hilbert space there exists a generator of a holomorphic semigroup which does not have…

We investigate the following fractional order in time Cauchy problem \begin{equation*} \begin{cases} \mathbb{D}_{t}^{\alpha }u(t)+Au(t)=f(u(t)), & 1<\alpha <2, \\ u(0)=u_{0},\,\,\,u^{\prime }(0)=u_{1}. & \end{cases}% \end{equation*}% where…

We study semigroups of convex monotone operators on spaces of continuous functions and their behaviour with respect to $\Gamma$-convergence. In contrast to the linear theory, the domain of the generator is, in general, not invariant under…

Projection operators arise naturally as one-particle density operators associated to Slater determinants in fields such as quantum mechanics and the study of determinantal processes. In the context of the semiclassical approximation of…

We study in this paper properties of functions of perturbed normal operators and develop earlier results obtained in \cite{APPS2}. We study operator Lipschitz and commutator Lipschitz functions on closed subsets of the plane. For such…

Let $X$ be a Banach space, and $T:[0,\infty)\rightarrow {\mathcal{L}}(X,X),$ the bounded linear operators on $X.$ A family $\{T(t)\}_{t\ge 0}\subseteq {% \mathcal{L}}(X,X)$ is called a one-parameter semigroup if $T(s+t)=T(s)T(t),$ and…

We develop the regularity theory for solutions to space-time nonlocal equations driven by fractional powers of the heat operator $$(\partial_t-\Delta)^su(t,x)=f(t,x),\quad\hbox{for}~0<s<1.$$ This nonlocal equation of order $s$ in time and…

We consider a class of non-trivial perturbations ${\mathscr A}$ of the degenerate Ornstein-Uhlenbeck operator in ${\mathbb R}^N$. In fact we perturb both the diffusion and the drift part of the operator (say $Q$ and $B$) allowing the…

We study some fundamental properties of semicocycles over semigroups of self-mappings of a domain in a Banach space. We prove that any semicocycle over a jointly continuous semigroup is itself jointly continuous. For semicocycles over…

In Euclidean space of dimension 2 or 3, we study a minimum time problem associated with a system of real-analytic vector fields satisfying H\"ormander's bracket generating condition, where the target is a nonempty closed set. We show that,…

The paper deals with continuous homomorphisms $S \ni s \mapsto T_s \in L(E)$ of amenable semigroups $S$ into the algebra $L(E)$ of all bounded linear operators on a Banach space $E$. For a closed linear subspace $F$ of $E$, sufficient…