On a class of holomorphic functions representable by Carleman formulas in the interior of an equilateral cone from their values on its rigid base

George Chailos, Alekos Vidras

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3 Citations (Scopus)
4 Downloads (Pure)

Abstract

Let Δ be an equilateral cone in C with vertices at the complex numbers 0, z1 0, z2 0 and rigid base M (Section 1). Assume that the positive real semi-axis is the bisectrix of the angle at the origin. For the base M of the cone Δ we derive a Carleman formula representing all those holomorphic functions f ∈ H (Δ) from their boundary values (if they exist) on M which belong to the class NHM 1 (Δ). The class NHM 1 (Δ) is the class of holomorphic functions in Δ which belong to the Hardy class H1 near the base M (Section 2). As an application of the above characterization, an important result is an extension theorem for a function f ∈ L1 (M) to a function f ∈ NHM 1 (Δ).

Original languageEnglish
Pages (from-to)657-672
Number of pages16
JournalJournal of Mathematical Analysis and Applications
Volume310
Issue number2
DOIs
Publication statusPublished - 15 Oct 2005

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Equilateral
Cones
Analytic function
Interior
Cone
Hardy Class
Extension Theorem
Complex number
Boundary Value
Angle
Class

Keywords

  • Carleman formula
  • Cone with a rigid base

Cite this

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AB - Let Δ be an equilateral cone in C with vertices at the complex numbers 0, z1 0, z2 0 and rigid base M (Section 1). Assume that the positive real semi-axis is the bisectrix of the angle at the origin. For the base M of the cone Δ we derive a Carleman formula representing all those holomorphic functions f ∈ H (Δ) from their boundary values (if they exist) on M which belong to the class NHM 1 (Δ). The class NHM 1 (Δ) is the class of holomorphic functions in Δ which belong to the Hardy class H1 near the base M (Section 2). As an application of the above characterization, an important result is an extension theorem for a function f ∈ L1 (M) to a function f ∈ NHM 1 (Δ).

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