### Abstract

Let sript U sign be a bounded, simply connected domain with Jordan rectifiable boundary and let M ⊂ ∂ sript U sign be an open analytic arc whose Lebesgue measure satisfies 0 < m(M) < m(∂ sript U sign. Our result gives a complete description of the class of holomorphic functions in sript U sign which are represented by the Carleman formulas on the open arc M, when ∂ sript U sign is almost regular with respect to M (Section 2). That is, we give a type of integral representation formulas for functions holomorphic in a domain sript U sign by its values on a part M of the boundary ∂ sript U sign. This class is denoted by sript N sign ℋ^{1} _{M}(sript U sign).

Original language | English |
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Pages (from-to) | 289-301 |

Number of pages | 13 |

Journal | Monatshefte fur Mathematik |

Volume | 149 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 2006 |

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### Keywords

- Analytic curves
- Carleman formulas
- Smirnov classes

### Cite this

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**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.** / Chailos, George; Vidras, Alekos.

Research output: Contribution to journal › Article

TY - JOUR

T1 - 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

AU - Chailos, George

AU - Vidras, Alekos

PY - 2006/12

Y1 - 2006/12

N2 - Let sript U sign be a bounded, simply connected domain with Jordan rectifiable boundary and let M ⊂ ∂ sript U sign be an open analytic arc whose Lebesgue measure satisfies 0 < m(M) < m(∂ sript U sign. Our result gives a complete description of the class of holomorphic functions in sript U sign which are represented by the Carleman formulas on the open arc M, when ∂ sript U sign is almost regular with respect to M (Section 2). That is, we give a type of integral representation formulas for functions holomorphic in a domain sript U sign by its values on a part M of the boundary ∂ sript U sign. This class is denoted by sript N sign ℋ1 M(sript U sign).

AB - Let sript U sign be a bounded, simply connected domain with Jordan rectifiable boundary and let M ⊂ ∂ sript U sign be an open analytic arc whose Lebesgue measure satisfies 0 < m(M) < m(∂ sript U sign. Our result gives a complete description of the class of holomorphic functions in sript U sign which are represented by the Carleman formulas on the open arc M, when ∂ sript U sign is almost regular with respect to M (Section 2). That is, we give a type of integral representation formulas for functions holomorphic in a domain sript U sign by its values on a part M of the boundary ∂ sript U sign. This class is denoted by sript N sign ℋ1 M(sript U sign).

KW - Analytic curves

KW - Carleman formulas

KW - Smirnov classes

UR - http://www.scopus.com/inward/record.url?scp=33845309445&partnerID=8YFLogxK

U2 - 10.1007/s00605-006-0401-0

DO - 10.1007/s00605-006-0401-0

M3 - Article

AN - SCOPUS:33845309445

VL - 149

SP - 289

EP - 301

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 4

ER -