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

Abstract

AbstractLet Δ be an equilateral cone in C with vertices at the complex numbers 0,z10,z20 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 NHM1(Δ). The class NHM1(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∈NHM1(Δ)