相关论文: An approximative approach to construction of the G…

We construct a correlation functions evolution corresponding to the Glauber dynamics in continuum. Existence of the corresponding strongly continuous contraction semigroup in a proper Banach space is shown. Additionally we prove the…

We develop a general, functional calculus approach to approximation of $C_0$-semigroups on Banach spaces by bounded completely monotone functions of their generators. The approach comprises most of well-known approximation formulas, yields…

We construct the time evolution for states of Glauber dynamics for a spatial infinite particle system in terms of generating functionals. This is carried out by an Ovsjannikov-type result in a scale of Banach spaces, leading to a local (in…

We consider the class of quantum mechanical master equations defined on a generic Banach space, arising by projecting weakly perturbed one-parameter groups of isometries. We show that the possible semigroup approximations are far from…

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…

Based on the convergence of their infinitesimal generators in the mixed topology, we provide a stability result for strongly continuous convex monotone semigroups on spaces of continuous functions. In contrast to previous results, we do not…

We describe a general approach to the construction of a state evolution corresponding to the Markov generator of a spatial birth-and-death dynamics in $\mathbb{R}^d$. We present conditions on the birth-and-death intensities which are…

In a series of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In particular, we introduced the notion of…

For nonuniform exponentially bounded evolution families on the half-line we introduce a class of Banach function spaces on which we define nonuniform evolution semigroups. We completely characterize nonuniform exponential stability in terms…

Contraction rates of time-varying maps induced by dynamical systems illuminate a wide range of asymptotic properties with applications in stability analysis and control theory. In finite-dimensional smoothly varying inner-product spaces…

We create a new, functional calculus, approach to approximation of C_0-semigroups on Banach spaces. As an application of this approach, we obtain optimal convergence rates in classical approximation formulas for C_0-semigroups. In fact, our…

In this paper, we study the existence of the random approximations and fixed points for random almost lower semicontinuous operators defined on finite dimensional Banach spaces, which in addition, are condensing or 1-set-contractive. Our…

Motivated by some recent twaddles on Mazur rotations problem, we study the "dynamics" of the semigroup of contractive automorphisms of Banach spaces, mostly in finite-dimensional spaces. We focus on the metric aspects of the "action" of…

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…

This paper is devoted to the construction and study of an equilibrium Glauber-type dynamics of infinite continuous particle systems. This dynamics is a special case of a spatial birth and death process. On the space $\Gamma$ of all locally…

We give a new proof of a characterization of the closeness of the range of a continuous linear operator and of the closeness of the sum of two closed vector subspaces of a Banach space. Then we state sufficient conditions for the closeness…

We introduce a new class of quasi-Banach spaces as an extension of the classical Grand Lebesgue Spaces for small values of the parameter, and we investigate some its properties, in particular, completeness, fundamental function, operators…

In this paper, we analyze recurrent $C_{0}$-semigroups of bounded operators on Banach spaces. We also introduce the notion of a (uniformly) $C_{0}$-rigid semigroups of bounded operators and give a structural characterization of them. A…

This work is devoted to the advanced study of Roper--Suffridge type extension operators. For a given non-normalized spirallike function (with respect to an interior or boundary point) on the open unit disk of the complex plane, we construct…

In this work I investigate uniformly continuous semigroups of sublinear transition operators on the Banach space of bounded real-valued functions on some countable set. I show how the family of exponentials of a bounded sublinear rate…