### Abstract

Let Δ be an equilateral cone in C with vertices at the complex numbers 0, z_{1} ^{0}, z_{2} ^{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 NH_{M} ^{1} (Δ). The class NH_{M} ^{1} (Δ) is the class of holomorphic functions in Δ which belong to the Hardy class H^{1} near the base M (Section 2). As an application of the above characterization, an important result is an extension theorem for a function f ∈ L^{1} (M) to a function f ∈ NH_{M} ^{1} (Δ).

Original language | English |
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Pages (from-to) | 657-672 |

Number of pages | 16 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 310 |

Issue number | 2 |

DOIs | |

Publication status | Published - 15 Oct 2005 |

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### Keywords

- Carleman formula
- Cone with a rigid base

### Cite this

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*Journal of Mathematical Analysis and Applications*, vol. 310, no. 2, pp. 657-672. https://doi.org/10.1016/j.jmaa.2005.02.036

**On a class of holomorphic functions representable by Carleman formulas in the interior of an equilateral cone from their values on its rigid base.** / Chailos, George; Vidras, Alekos.

Research output: Contribution to journal › Article

TY - JOUR

T1 - On a class of holomorphic functions representable by Carleman formulas in the interior of an equilateral cone from their values on its rigid base

AU - Chailos, George

AU - Vidras, Alekos

PY - 2005/10/15

Y1 - 2005/10/15

N2 - 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).

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).

KW - Carleman formula

KW - Cone with a rigid base

UR - http://www.scopus.com/inward/record.url?scp=24044472411&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2005.02.036

DO - 10.1016/j.jmaa.2005.02.036

M3 - Article

AN - SCOPUS:24044472411

VL - 310

SP - 657

EP - 672

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -