dc.contributor.author | Aizenberg, L. | en |
dc.contributor.author | Vidras, Alekos | en |
dc.creator | Aizenberg, L. | en |
dc.creator | Vidras, Alekos | en |
dc.date.accessioned | 2019-12-02T10:33:22Z | |
dc.date.available | 2019-12-02T10:33:22Z | |
dc.date.issued | 2002 | |
dc.identifier.issn | 0025-584X | |
dc.identifier.uri | http://gnosis.library.ucy.ac.cy/handle/7/56359 | |
dc.description.abstract | Carleman formulas, unlike the Cauchy formula, restore a function holomorphic in a domain D by its values on a part M of the boundary ∂D, provided that M is of positive Lebesgue measure. An extensive survey of Carleman formulas is found in [AIZ]. In the present paper new Carleman formulas are obtained for domains in ℂn and the question about a description of the class of holomorphic functions that are represented by Carleman formula is investigated. In [AIZTV] we considered the simplest Carleman formulas in one and several complex variables on particular simply connected domains. It was shown there that a necessary and sufficient condition for a holomorphic function f to be represented by Carleman formula over the set M is that f must belong to "the Hardy class ℋ1 near the set M". In the present paper we look at the case of Fok-Kuni integral representation formula. This is a particular form of abstract Carleman formula, but it involves simply connected domains, not covered by previous results. Furthermore we initiate the study of the same questions for non-simply connected domains. We obtain the description of the class of functions representable by Carleman formula on annulii in ℂ and their generalizations, the Reinhardt domains in ℂn. | en |
dc.source | Mathematische Nachrichten | de |
dc.source.uri | https://www.scopus.com/inward/record.uri?eid=2-s2.0-0036066654&doi=10.1002%2f1522-2616%28200204%29237%3a1%3c5%3a%3aAID-MANA5%3e3.0.CO%3b2-F&partnerID=40&md5=c24678fa8cc74930f5f2b11291b0e9bd | |
dc.subject | Analytic continuation | en |
dc.subject | Carleman formulas | en |
dc.title | On Carleman formulas and on the class of holomorphic functions representable by them | en |
dc.type | info:eu-repo/semantics/article | |
dc.identifier.doi | 10.1002/1522-2616(200204)237:1<5 | |
dc.description.volume | 237 | |
dc.description.startingpage | 5 | |
dc.description.endingpage | 25 | |
dc.author.faculty | Σχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied Sciences | |
dc.author.department | Τμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics | |
dc.type.uhtype | Article | en |
dc.description.notes | <p>Cited By :5</p> | en |
dc.source.abbreviation | Math.Nachr. | de |
dc.contributor.orcid | Vidras, Alekos [0000-0001-9917-8367] | |
dc.gnosis.orcid | 0000-0001-9917-8367 | |