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Building on techniques developed by Cowen and Gallardo-Guti{e}rrez, we find a concrete formula for the adjoint of a composition operator with rational symbol acting on the Hardy space $H^{2}$. We consider some specific examples, comparing our formula with several results that were previously known.
In this paper we {em discuss} diverse aspects of mutual relationship between adjoints and formal adjoints of unbounded operators bearing a matrix structure. We emphasize on the behaviour of row and column operators as they turn out to be the germs of
Suppose that $phi$ and $psi$ are smooth complex-valued functions on the circle that are invertible, have winding number zero with respect to the origin, and have meromorphic extensions to an open neighborhood of the closed unit disk. Let $T_phi$ and
We study a semigroup of weighted composition operators on the Hardy space of the disk $H^2(mathbb{D})$, and more generally on the Hardy space $H^2(U)$ attached to a simply connected domain $U$ with smooth boundary. Motivated by conformal field theory
We study topologizability and power boundedness of weigh-ted composition operators on (certain subspaces of) $mathscr{D}(X)$ for an open subset $X$ of $mathbb{R}^d$. For the former property we derive a characterization in terms of the symbol and the
We investigate (uniform) mean ergodicity of (weighted) composition operators on the space of smooth functions and the space of distributions, respectively, both over an open subset of the real line. Among other things, we prove that a composition ope