Generation of analytic semigroups by generalized Ornstein–Uhlenbeck operators with potentials

Generation of Equicontinuous Semigroups by Hermitian and Sectorial Operators. I

Semiflow of analytic functions and semigroups of composition operators

Abstract The study of analytic semiflows on the open unit disc and the particular form of its infinitesimal generator G makes possible the study of semigroups of composition operators (T (t))t≥0 on various well-known spaces of holomorphic functions such as Hardy, Dirichlet and Bergman spaces. We will provide compactness, analyticity and invertibility complete characterization of (T (t))t≥0 in t...

Semigroups of Weighted Composition Operators in Spaces of Analytic Functions

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...

Integrodifferential Equations with Analytic Semigroups

In this paper we study a class of integrodifferential equations considered in an arbitrary Banach space. Using the theory of analytic semigroups we establish the existence, uniqueness, regularity and continuation of solutions to these integrodifferential equations.

Generalized Ladder Operators for Shape-invariant Potentials

A general form for ladder operators is used to construct a method to solve bound-state Schrödinger equations. The characteristics of supersymmetry and shape invariance of the system are the start point of the approach. To show the elegance and the utility of the method we use it to obtain energy spectra and eigenfunctions for the one-dimensional harmonic oscillator and Morse potentials and for ...