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Approximation of holomorphic mappings on 1-convex domainsStopar, KrisNaj bo ▫$\pi: Z \to X$▫ holomorfna submerzija kompleksne mnogoterosti ▫$Z$▫ na kompleksno mnogoterost ▫$X$▫ in ▫$D \Subset X$▫ 1-konveksna domena s strogo psevdokonveksnim robom. Dokažemo, da pod ... določenimi pogoji vedno obstaja sprej ▫$\pi$▫-prerezov nad ▫$\bar{D}$▫, ki ima predpisano jedro, fiksira izjemno množico ▫$E$▫ domene ▫$D$▫ in je dominanten na ▫$\bar{D} \setminus E$▫. Vsak prerez v tem spreju je razreda ▫$C^k(\bar{D})$▫ in holomorfen na ▫$D$▫. Kot posledico dobimo več aproksimacijskih rezultatov za ▫$\pi$▫-prereze. V posebnem dokažemo, da lahko ▫$\pi$▫-prereze, ki so rezreda ▫$C^k(\bar{D})$▫ in holomorfni na ▫$D$▫, aproksimiramo v ▫$C^k(\bar{D})$▫ topologiji s ▫$\pi$▫-prerezi, ki so holomorfni v odprtih okolicah domene ▫$\bar{D}$▫. Pod dodatnimi predpostavkami na submerzijo dobimo tudi aproksimacijo z globalnimi holomorfnimi ▫$\pi$▫-prerezi in Oka princip nad 1-konveksnimi mnogoterostmi. Omenimo tudi aplikacijo pri konstrukciji pravih holomorfnih preslikav 1-konveksnih domen v ▫$q$▫-konveksne mnogoterosti.Source: International journal of mathematics. - ISSN 0129-167X (Vol. 24, no. 14, 2014, 1350108 [33 str.])Type of material - article, component partPublish date - 2014Language - englishCOBISS.SI-ID - 16894553
Author
Stopar, Kris
Topics
matematika |
kompleksna analiza |
1-konveksna domena |
Cartanov par |
Cartanova lema |
sprej |
sprej prerezov |
aproksimacija |
mathematics |
complex analysis |
1-convex domain |
Cartan pair |
Cartan lemma |
spray |
spray of sections |
approximation
source: International journal of mathematics. - ISSN 0129-167X (Vol. 24, no. 14, 2014, 1350108 [33 str.])
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Stopar, Kris | 32027 |
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