Related papers: Linear maps preserving inner functions

We characterize in various ways the weighted composition transformations which preserve the class ${\mathcal P}$ of normalized analytic functions in the disk with positive real part. We analyze the meaning of the criteria obtained for…

We present a family of sense-preserving harmonic mappings in the unit disk related to the classical generalized (analytic) Koebe functions. We prove that these are precisely the mappings that maximize simultaneously the real part of every…

Under very general conditions it is shown that if $A$ is a uniform algebra generated by real-analytic functions, then either $A$ consists of all continuous functions or else there exists a disc on which every function in $A$ is holomorphic.…

In this note we study the problem of determining the holomorphic self maps of the unit disc that induce a bounded composition operator on Dirichlet-type spaces. We find a class of symbols $\varphi$ that induce a bounded composition operator…

Let g be an analytic function on the open unit disc U such that g(U) is contained in U, and let h be an analytic function on U such that the weighted composition operator W_{h,g) defined by W_{h,g}f = h f(g) is bounded on the Hardy space…

We prove that the Bernardi Integral Operator maps certain classes of bounded starlike functions into the class of convex functions, improving the result of Oros and Oros. We also present a general unified method for investigating various…

By means of hypercyclic operator theory, we complement our previous results on hypercyclic holomorphic maps between complex Euclidean spaces having slow growth rates,by showing {\it abstract abundance} rather than {\it explicit existence}.…

Denote by $B_n$ the set of complex square matrices of order $n$, whose Euclidean operator norms are $<1$. Its Shilov boundary is the set $U(n)$ of all unitary matrices. A holomorphic map $B_m\to B_n$ is inner if it sends $U(m)$ to $U(n)$.…

Let U be the closed unit disc in C and let p be a point on the unit circle. Let f be a continuous function on U which extends holomorphically from each circle contained in U and centered at the origin, and from each circle contained in U…

Every diagonalmatrix D yields an endomorphism on the n-dimensional complex vectorspace. If one provides this space with Hoelder norms, we can compute the operator norm of D. We define homogeneous weighted spaces as a generalization of…

Given a holomorphic self-map $\varphi$ of $\D$ (the open unit disc in $\mathbb{C}$), the composition operator $C_{\varphi} f = f \circ \varphi$, $f \in H^2(\mathbb{\D})$, defines a bounded linear operator on the Hardy space…

The main purpose of this paper is to derive some subordination and superordination results involving certain of integral operator for meromorphic univalent functions in the punctured open unit disk. Several sandwich-type results are also…

We study composition operators between weighted Bergman spaces of the polydisc induced by smooth symbols. We prove a general result of continuity which only involves the behaviour of the symbol on the polytorus. We deduce from this several…

We describe the proper closed invariant subspaces of the integration operator when it acts continuously on countable intersections and countable unions of weighted Banach spaces of holomorphic functions on the unit disc or the complex…

We study topological transitivity/hypercyclicity and topological (weak) mixing for weighted composition operators on locally convex spaces of scalar-valued functions which are defined by local properties. As main application of our general…

We investigate some types of composition operators, linear and not, and conditions for some spaces to be mapped into themselves and for the operators to satisfy some good properties.

A d.c. (delta-convex) function on a normed linear space is a function representable as a difference of two continuous convex functions. We show that an infinite dimensional analogue of Hartman's theorem on stability of d.c. functions under…

In a recent paper, Horel-Krannich-Kupers proved that all endomorphisms of the little $d$-disk operad are automorphisms. In this paper we show that this is also true for the framed little $d$-disk operad by using the classification of self…

In this paper first we give a partial answer to a question of L. Moln\'ar and W. Timmermann. Namely, we will describe those linear (not necessarily bijective) transformations on the set of self-adjoint matrices which preserve a unitarily…

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent…