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Holomorfni spreji v kompleksni analizi in geometriji : doktorska disertacijaStopar, KrisNaj bo ▫$\pi \colon Z \to X$▫ holomorfna submerzija iz kompleksne mnogoterosti ▫$Z$▫ na kompleksno mnogoterost ▫$X$▫ in ▫$D \Subset X$▫ 1-konveksna domena s strogo psevdokonveksnim robom. V ... disertaciji dokažemo, da pod določenimi predpostavkami 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 ▫${\mathcal C}^k(\bar{D})$▫ in holomorfen na ▫$D$▫. Kot posledico dobimo več aproksimacijskih rezultatov za ▫$\pi$▫-prereze. Med drugim dokažemo, da lahko ▫$\pi$▫-prereze, ki so razreda ▫${\mathcal C}^k(\bar{D})$▫ in holomorfni na ▫$D$▫ aproksimiramo v ▫${\mathcal C}^k(\bar{D})$▫ topologiji s ▫$\pi$▫-prerezi, ki so holomorfni v odprtih okolicah množice ▫$\bar{D}$▫. Pod dodatnimi predpostavkami na submerzijo dobimo tudi aproksimacijo z globalnimi holomorfnimi ▫$\pi$▫-prerezi in princip Oka nad 1-konveksnimi mnogoterostmi. Vključimo tudi rezultat o obstoju pravih holomorfnih preslikav iz 1-konveksnih domen v ▫$q$▫-konveksne mnogoterosti.Type of material - dissertation ; adult, seriousPublication and manufacture - Ljubljana : [K. Stopar], 2013Language - slovenianCOBISS.SI-ID - 16765529
Link(s):
http://www.matknjiz.si/doktorati/2013/StoparK-14521-5.pdf
Repository of the University of Ljubljana – RUL
Digitalna knjižnica Slovenije - dLib.siDostop z namenskih računalnikov v prostorih NUK
Author
Stopar, Kris
Other authors
Prezelj, Jasna
Topics
1-konveksna domena |
1-konveksen Cartanov par |
Cartanova lema |
sprej |
sprej prerezov |
aproksimacija |
princip Oka |
prava holomorfna preslikava |
1-convex domain |
1-convex Cartan pair |
Cartan lemma |
spray |
spray of sections |
approximation |
Oka principle |
proper holomorphic map
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FMF and IMFM, Mathematical Library, Ljubljana | Ljubljana | MAKLJ |
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National and University Library, Ljubljana | Ljubljana | NUK |
reading room 1 cop.
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not for loan 1 cop.
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Database name | Field | Year |
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Stopar, Kris | 32027 |
Prezelj, Jasna | 20821 |
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