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}
}
• Published 2013
• Mathematics
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…
2 Citations
Cauchy–Fantappiè Integral Formula for Holomorphic Functions on Special Tube Domains in $$\mathbb {C}^2$$C2
• Mathematics
Complex Analysis and Operator Theory
• 2018
Let $$T_{B}=\mathbb {R}^2\times i\{(y_1,y_2)\in \mathbb {R}^2 :y_1^2+y_2^2 <1\}$$TB=R2×i{(y1,y2)∈R2:y12+y22<1} be the tube in $$\mathbb {C}^2$$C2 with base the imaginary disk B=i\{(y_1,y_2)\in
An optimal investment and risk control policy for a bank under exponential utility
ABSTRACT Motivated by the Basel Capital Accord Requirement (CAR), we analyze a risk control portfolio selection problem under exponential utility when a banker faces both Brownian and jump risks. The

References

SHOWING 1-10 OF 33 REFERENCES
The class of holomorphic functions representable by Carleman formula
• Mathematics
• 1998
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
• Mathematics
• 2007
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
• Mathematics
• 2006
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
• Mathematics
• 2004
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
• Mathematics
• 1997
Preliminaries 1. Banach spaces and Metric Linear Spaces 2. Spectral of Theory Linear Operators 3. Frechet Spaces and their Dual Spaces
Progress in mathematics
• Mathematics
• 1979
Over four decades David Vogan’s groundbreaking work in representation theory has changed the face of the subject. We give a brief summary here.