Duality and the Class of Holomorphic Functions Representable by Carleman ’ s Formula

@inproceedings{Azenberg2013DualityAT,
  title={Duality and the Class of Holomorphic Functions Representable by Carleman ’ s Formula},
  author={Lev Abramovich Aĭzenberg and Alekos Vidras},
  year={2013}
}
The purpose of the present paper is two-fold. The first is to describe the space of continuous functionals for the Smirnov space Ep(U), p ≥ 1, when U is a simply connected, bounded domain with Ahlfors regular boundary in terms of functions which are analytic in the complement U (or dual complement) and have a prescribed boundary behavior on ∂U . As an application of the above results, we give a precise description of the space of continuous functionals acting on the space NH M (U), p ≥ 1 of… 
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References

SHOWING 1-10 OF 33 REFERENCES
The class of holomorphic functions representable by Carleman formula
Carleman formulas, unlike the Cauchy formula, restore a function holomorphic in a domain D by its values on a part M of the boundary aD, provided that M is of positive Lebesgue measure. Naturally
On a class of holomorphic functions representable by Carleman formulas in the disk from their values on the arc of the circle
Let D be a unit disk andM be an open arc of the unit circle whose Lebesgue measure satisfies 0 < l (M) < 2π. Our first result characterizes the restriction of the holomorphic functions f ∈ ℋ︁(D),
The topology of the class of functions representable by Carleman type formulae, duality and applications
We set D to be a simply connected domain and we consider exhaustion function spaces, X∞(D) with the projective topology (see §1). We show that the natural topology on the topological dual of X∞(D),
On a Class of Holomorphic Functions Representable by Carleman Formulas in Some Class of Bounded, Simply Connected Domains From Their Values on an Analytic Arc
Abstract.Let ${\cal U}$ be a bounded, simply connected domain with Jordan rectifiable boundary and let $ M \subset \partial {\cal U}$ be an open analytic arc whose Lebesgue measure satisfies $ 0 <
Complex Convexity and Analytic Functionals
1 Convexity in Real Projective Space.- 1.1 Convexity in real affine space.- 1.2 Real projective space.- 1.3 Convexity in real projective space.- 2 Complex Convexity.- 2.1 Linearly convex sets.- 2.2
Introduction to Functional Analysis
Preliminaries 1. Banach spaces and Metric Linear Spaces 2. Spectral of Theory Linear Operators 3. Frechet Spaces and their Dual Spaces
Progress in mathematics
Over four decades David Vogan’s groundbreaking work in representation theory has changed the face of the subject. We give a brief summary here.
Sur la topologie des espaces de fonctions holomorphes
Function theory in polydiscs
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