Weighted Composition Operators from Hardy Spaces to Weighted-Type Spaces on the Upper Half-Plane

Let the holomorphic mapping ?, and the holomorphic self-map ? are on the upper half-plane. We characterize bounded weighted composition operators between the Hardy space and the weighted-type space on the upper half-plane, and we study the special cases when which is the Hilbert space. Under a mild condition on ?; we also show the compactness of these operators and there special cases. Keywords: Weighted composition operators, Hardy spaces, weighted type spaces, upper half plane

An Inverse Problem for Localization Operators

A classical result of time-frequency analysis, obtained by I. Daubechies in 1988, states that the eigenfunctions of a time-frequency localization operator with circular localization domain and Gaussian analysis window are the Hermite functions. In this contribution, a converse of Daubechies' theorem is proved. More precisely, it is shown that, for simply connected localization domains, if one of the eigenfunctions of a time-frequency localization operator with Gaussian window is a Hermite function, then its localization domain is a disc. The general problem of obtaining, from some knowledge of its eigenfunctions, information about the symbol of a time-frequency localization operator, is denoted as the inverse problem, and the problem studied by Daubechies as the direct problem of time-frequency analysis. Here, we also solve the corresponding problem for wavelet localization, providing the inverse problem analogue of the direct problem studied by Daubechies and Paul.Comment: 18 pages, 1 figur

Local properties of Hilbert spaces of Dirichlet series

We show that the asymptotic behavior of the partial sums of a sequence of positive numbers determine the local behavior of the Hilbert space of Dirichlet series defined using these as weights. This extends results recently obtained describing the local behavior of Dirichlet series with square summable coefficients in terms of local integrability, boundary behavior, Carleson measures and interpolating sequences. As these spaces can be identified with functions spaces on the infinite-dimensional polydisk, this gives new results on the Dirichlet and Bergman spaces on the infinite dimensional polydisk, as well as the scale of Besov-Sobolev spaces containing the Drury-Arveson space on the infinite dimensional unit ball. We use both techniques from the theory of sampling in Paley-Wiener spaces, and classical results from analytic number theory.Comment: 27 pages, 1 figur

On Laplace-Carleson embedding theorems

This paper gives embedding theorems for a very general class of weighted Bergman spaces: the results include a number of classical Carleson embedding theorems as special cases. We also consider little Hankel operators on these Bergman spaces. Next, a study is made of Carleson embeddings in the right half-plane induced by taking the Laplace transform of functions defined on the positive half-line (these embeddings have applications in control theory): particular attention is given to the case of a sectorial measure or a measure supported on a strip, and complete necessary and sufficient conditions for a bounded embedding are given in many cases.Comment: 26 pages, 1 figur

Compact Composition Operators between Hardy Spaces

We characterise composition operators between Hardy spaces. Certain growth conditions for generalized Nevanlinna counting functions of the inducing map are shown to be necessary and sufficient for such operators to be bounded or compact. Under a mind condition we show that a composition operators Cj is compact on the Hardy spaces of the open unit ball in .   Keywords: Hardy Spaces, composition operators, boundedness, Compactness, Nevanlinna counting functions

A class of quasicontractive semigroups acting on Hardy and Dirichlet space

This paper provides a complete characterization of quasicontractive C0-semigroups on Hardy and Dirichlet space with a prescribed generator of the form Af = Gf ′. We show that such semigroups are semigroups of composition operators, and we give simple sufficient and necessary condition on G. Our techniques are based on ideas from semigroup theory, such as the use of numerical ranges

Carleson embeddings and pointwise multipliers between Hardy-Orlicz spaces and Bergman-Orlicz spaces of the upper half-plane

In this article, we give a general characterization of Carleson measures involving concave or convex growth functions. We use this characterization to establish continuous injections and also to characterize the set of pointwise multipliers between Hardy-Orlicz spaces and Bergman-Orlicz spaces.Comment: 30 page