We study the strong continuity of weighted composition semigroups of the form Ttf = φ′t (f ◦ φt) in several spaces of analytic functions. First we give a general result on separable spaces and use it to prove that these semigroups are always strongly continuous in the Hardy and Bergman spaces. Then we focus on two non-separable family of spaces, the mixed norm and the weighted Banach spaces. We...

In this paper we establish a relation between the notion of operators of analytic semigroups and matrix transformations from a set of sequences into w∞. We get extensions of some results given by Labbas and de Malafosse concerning applications of the sum of operators in the nondifferential case.

gives rise to a well-defined propagator, which is a semigroup of linear operators, and the theory of semigroups of linear operators on Banach spaces has developed quite rapidly since the discovery of the generation theorem byHille and Yosida in 1948. By now, it is a rich theory with substantial applications to many fields cf., e.g., 1–6 . In this paper, we pay attention to some basic problems o...

A class of functions is speciied which give rise to semibounded quadratic forms on weighted Bergman spaces and thus can be interpreted as symbols of self-adjoint Berezin-Toeplitz operators. A similar class admits a probabilistic expression of the sesqui-analytic integral kernel for the associated semigroups. Both results are the consequence of a relation of Berezin-Toeplitz operators to Schrr o...

(1) Background: This paper is devoted to the study of a class semilinear initial boundary value problems parabolic type. (2) Methods: We make use fractional powers analytic semigroups and interpolation theory compact linear operators due Lions–Peetre. (3) Results: give functional proof C2 compactness bounded regular solution orbit for with Dirichlet, Neumann Robin conditions. (4) Conclusions: A...

In this paper we shall study a fractional integral equation in an arbitrary Banach space X . We used the analytic semigroups theory of linear operators and the fixed point method to establish the existence and uniqueness of solutions of the given problem.We also prove the existence of global solution. The existence and convergence of the Faedo–Galerkin solution to the given problem is also prov...

This paper is concerned with characterizations of those linear, closed, but not necessarily densely defined operators A on a Banach space E with nonempty resolvent set for which the abstract Cauchy problem u'(t) = Au(t), u(0) = x has unique, exponentially bounded solutions for every initial value x e D(A). Investigating these operators we are led to the class of "integrated semigroups". Among o...