### Abstract

Original language | English |
---|---|

Pages (from-to) | 1117-1128 |

Number of pages | 12 |

Journal | Complex Variables, Theory and Applications |

Volume | 49 |

Issue number | 15 |

Publication status | Published - 2004 |

### Fingerprint

### Keywords

- Hardy classes
- Carleman formulas
- Operator valued Holomorphic Functions

### Cite this

}

*Complex Variables, Theory and Applications*, vol. 49, no. 15, pp. 1117-1128.

**Vector and operator valued holomorphic functions representable by Carleman type formulas.** / Chailos, George.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Vector and operator valued holomorphic functions representable by Carleman type formulas

AU - Chailos, George

PY - 2004

Y1 - 2004

N2 - Let be a simply connected domain and let M be a connected subset of its boundary of positive Lebesque measure. With X we denote a separable Hilbert space or the space of bounded linear functionals on . We set f to be an X-valued holomorphic function, and with we denote the class of X-valued holomorphic functions on which belong to the Hardy class near the set M. In our main result, we show that if f belongs to Near Hardy Class, then f is representable by a Carleman type formula, and conversely, if f is representable by a Carleman type formula, and in some sense has an analytic continuation across M, then f belongs to the above Near Hardy class . Furthermore we show that in general Near hardy and classical Hardy classes do not coincide.

AB - Let be a simply connected domain and let M be a connected subset of its boundary of positive Lebesque measure. With X we denote a separable Hilbert space or the space of bounded linear functionals on . We set f to be an X-valued holomorphic function, and with we denote the class of X-valued holomorphic functions on which belong to the Hardy class near the set M. In our main result, we show that if f belongs to Near Hardy Class, then f is representable by a Carleman type formula, and conversely, if f is representable by a Carleman type formula, and in some sense has an analytic continuation across M, then f belongs to the above Near Hardy class . Furthermore we show that in general Near hardy and classical Hardy classes do not coincide.

KW - Hardy classes

KW - Carleman formulas

KW - Operator valued Holomorphic Functions

M3 - Article

VL - 49

SP - 1117

EP - 1128

JO - Complex Variables, Theory and Applications

JF - Complex Variables, Theory and Applications

SN - 1747-6941

IS - 15

ER -