The Dirichlet space D consists of all analytic functions f defined on the unit disk with âˆ« |f (z)|dA < âˆž. The space of multipliers MD consists of analytic functions Ï† with Ï†f âˆˆ D for all f âˆˆ D. Aâ€¦ (More)

Using recent results of J~rai we show that the measurable solutions of the functional equation f ( x l y 1 . . . . . x,,y.)f((1 x0(1 Y0 ..... (1 x.)(l y.)) =f(xl(1 Yl) ..... x,(1 y.))fOq(l x 0 .....â€¦ (More)

In this paper we study extremal functions for invariant subspaces Ji of the Dirichlet shift, i.e., solutions <p of the extremal problem Â»up{|/"Â»(0)|/||/||fl:/eur, /VO}. Here n is the smallestâ€¦ (More)

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral. This is a remark about the zerosâ€¦ (More)

Let k be the reporducing kernel for a Hilbert space H(k) of nanlytic functions on Bd, the open unit ball in C, d â‰¥ 1. k is called a complete NP kernel, if k0 â‰¡ 1 and if 1 âˆ’ 1/kÎ»(z) is positiveâ€¦ (More)

For a Hilbert space H of functions let H H be the space of weak products of functions in H, i.e. all functions h that can be written as h = âˆ‘âˆž i=1 figi for some fi, gi âˆˆ H with âˆ‘âˆž i=1 â€–fiâ€–â€–giâ€– <âˆž.â€¦ (More)

Consider the subspaces La(Ï‰) and L 2 h(Ï‰) of L (Ï‰) consisting of those functions that can be altered on null sets so as to be analytic and harmonic on D, respectively. If two harmonic functions on Dâ€¦ (More)

Let Î¼ be a finite positive measure on the closed disk D in the complex plane, let 1 â‰¤ t < âˆž, and let P t(Î¼) denote the closure of the analytic polynomials in Lt(Î¼). We suppose that D is the set ofâ€¦ (More)

Let H be a Hilbert space of analytic functions on the open unit disc D such that the operator MÎ¶ of multiplication with the identity function Î¶ defines a contraction operator. In terms of theâ€¦ (More)