Related papers: A note on perturbations of $C_0$-semigroups

We consider the approximation to an abstract evolution problem with inhomogeneous side constraint using $A$-stable Runge-Kutta methods. We derive a priori estimates in norms other than the underlying Banach space. Most notably, we derive…

We characterise contractivity, boundedness and polynomial boundedness for a C_0-semigroup on a Banach space in terms of its cogenerator V (or the Cayley transform of the generator) or its resolvent. In particular, we extend results of…

We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness assumptions of the underlying Banach norm. We use this inequality in order…

This article is devoted to the stability of error bounds (local and global) for semi-infinite convex constraint systems in Banach spaces. We provide primal characterizations of the stability of local and global error bounds when systems are…

In this paper, we deal with a notion of Banach space-valued mappings defined on a set consisting of finite graphs with uniformly bounded vertex degree. These functions will be endowed with certain boundedness and additivity criteria. We…

We prove various notions of uniform continuity for compact-quantum-group representations on Hilbert or Banach spaces equivalent to having finite spectrum, i.e. finitely many isotypic components. This generalizes the classical analogue for…

This article focuses on a new concept of quadratic variation for processes taking values in a Banach space $B$ and a corresponding covariation. This is more general than the classical one of M\'etivier and Pellaumail. Those notions are…

Let $UC(K)$ denote the Banach space of all bounded uniformly continuous functions on a hypergroup $K$. The main results of this article concern on the $\alpha$-amenability of $UC(K)$ and quotients and products of hypergroups. It is also…

The aim of this paper is to present some results about generation, sectoriality and gradient estimates both for the semigroup and for the resolvent of suitable realizations of the operators [\Ab u(x)=\gamma xu"(x) + b u'(x),] with constants…

In this paper, we are concerned with backward solvabilities of heat equations, in an abstract framework. We show that semigroups $T_t$ in Banach spaces $X$, generated by heat operators, are extendable to groups in an extended space $E$,…

We investigate the stability properties of strongly continuous semigroups generated by operators of the form $A-BB^\ast$, where $A$ is a generator of a contraction semigroup and $B$ is a possibly unbounded operator. Such systems arise…

In this work we construct certain general bundles $<\mathfrak{M},\rho,X>$ and $<\mathfrak{B},\eta,X>$ of Hausdorff locally convex spaces associated with a given Banach bundle $<\mathfrak{E},\pi,X>$. Then we present conditions ensuring the…

We prove variation and oscillation $L^p$-inequalities associated with fractional derivatives of certain semigroups of operators and with the family of truncations of Riesz transforms in the inverse Gaussian setting. We also study these…

In this paper we show that two-sided heat kernel estimates for a class of (not necessarily symmetric) diffusions with jumps are stable under non-local Feynman-Kac perturbations.

We study relations between the decaying rates of operator semigroups on Hilbert spaces and some spectral properties of their respective generators; in particular, we show that the decaying rates of orbits of semigroups which are stable but…

We consider Laplacians acting on sections of homogeneous vector bundles over symmetric spaces. By using an integral representation of the heat semi-group we find a formal solution for the heat kernel diagonal that gives a generating…

In this paper we study the preservation of strong stability of strongly continuous semigroups on Hilbert spaces. In particular, we study a situation where the generator of the semigroup has a finite number of spectral points on the…

This paper studies Brownian motion and heat kernel measure on a class of infinite dimensional Lie groups. We prove a Cameron-Martin type quasi-invariance theorem for the heat kernel measure and give estimates on the $L^p$ norms of the…

The existence of a solution, convergence and stability of the penalty method for variational inequalities with nonsmooth unbounded uniformly and properly monotone operators in Banach spase $B$ are investigated. All the objects of the…

In this article, the existence of the spectrum (the eigenvalues) for the nonlinear continuous operators acting in the Banach spaces is investigated. For the study, this question is used a different approach that allows the studying of all…