If A is a unital weak-∗ closed subalgebra of a multiplier algebra on a reproducing kernel Hilbert space which has property A1(1), then the cyclic invariant subspaces provide an Nevanlinna-Pick (NP) family of kernels. This yields an NP interpolation theorem for a wide class of operator algebras. In particular, it applies to many kernel spaces over the unit disk including the Bergman space. We al...

Let f and g be two nonconstant meromorphic functions defined in the open complex plane C. If for some a ∈ C∪ {∞}, f − a and g − a have the same set of zeros with the same multiplicities, we say that f and g share the value a CM (counting multiplicities), and if we do not consider the multiplicities, then f and g are said to share the value a IM (ignoring multiplicities). We denote by T(r) the m...

We extend the standard Fourier multiplier result to square integrable functions with values in (possibly nonseparable) Hilbert spaces. As a corollary, we extend the standard Hardy class boundary trace result to H (even Nevanlinna or bounded type) functions whose values are bounded linear operators between Hilbert spaces. Both results have been well-known in the case that the Hilbert spaces are ...

This paper gives several different ways in which operator norms characterize those composition operators Cφ that arise from holomorphic self-maps φ of the unit disc that are inner functions. The setting is the Hardy space H of the disc, and the key result is a characterization of inner functions in terms of the asymptotic behavior of the Nevanlinna counting function.

In the paper we compare the relative Valiron defect with the relative Nevanlinna defect of a meromorphic function or a transcendental meromorphic function on the basis of sharing of values of them. Mathematics Subject Classification: 30D35, 30D30

The non-commutative analytic Toeplitz algebra is the wot–closed algebra generated by the left regular representation of the free semigroup on n generators. We obtain a distance formula to an arbitrary wotclosed right ideal and thereby show that the quotient is completely isometrically isomorphic to the compression of the algebra to the orthogonal complement of the range of the ideal. This is us...

Nous montrons la densité des cycles répulsifs dans l’ensemble de Julia des fonctions méromorphes transcendantes à une variable complexe, sans utiliser le théorème des cinq ı̂les d’Ahlfors ni la théorie de Nevanlinna.

We give analytic Carleson-type characterisations of the interpolating sequences for the Nevanlinna and Smirnov classes. From this we deduce necessary and sufficient geometric conditions, both expressed in terms of a certain non-tangential maximal function associated to the sequence. Some examples show that the gap between the necessary and the sufficient conditions cannot be covered. We also di...

This paper deals with the indeterminate moment problem on the real line. We are given a positive measure μ on R having moments of all orders and we assume that μ is not determined by its moments. For details about the indeterminate moment problem see the monographs by Akhiezer, by Shohat and Tamarkin or the survey paper by Berg. Our notation follows that of Akhiezer. In this indeterminate situa...

New special types of stationary conservative impedance and scattering systems, the so-called non-canonical systems, involving triplets of Hilbert spaces and projection operators, are considered. It is established that every matrix-valued Herglotz-Nevanlinna function of the form