473 KB0 KB0 KB2013Prezelj-Perman, JasnaStopar, Kris72 str., 30 cmCOBISSID:16765529PID:https://repozitorij.uni-lj.si/IzpisGradiva.php?id=95850URN:URN:NBN:SI:doc-LLT0UKKUslK. Stoparvisokošolska dela1-convex Cartan pair1-convex domain1-konveksen Cartanov par1-konveksna domenaapproximationaproksimacijaCartan lemmaCartanova lemaDisertacijeHolomorfni spreji (matematika)Oka principleprava holomorfna preslikavaprincip Okaproper holomorphic mapsprayspray of sectionssprejsprej prerezovHolomorfni spreji v kompleksni analizi in geometriji| doktorska disertacija|Let ?$\pi \colon Z \to X$? be a holomorphic submersion of a complex manifold ?$Z$? onto a complex manifold ?$X$? and ?$D \Subset X$? a 1-convex domain with strongly pseudoconvex boundary. We prove that under certain conditions there always exists a spray of ?$\pi$?-sections over ?$\bar{D}$? which has prescribed core, fixes the exceptional set ?$E$? of ?$D$?, and is dominating on ?$\bar{D} \setminus E$?. Each section in this spray is of class ?${\mathcal C}^k(\bar{D})$? and holomorphic on ?$D$?. As a consequence we obtain several approximation results for ?$\pi$?-sections. In particular, we prove that ?$\pi$?-sections which are of class ?${\mathcal C}^k(\bar{D})$? and holomorphic on ?$D$? can be approximated in the ?${\mathcal C}^k(\bar{D})$? topology by ?$\pi$?-sections that are holomorphic in open neighborhoods of ?$\bar{D}$?. Under additional assumptions on the submersion we also get approximation by global holomorphic ?$\pi$?-sections and the Oka principle over 1-convex manifolds. We include a result on the existance of proper holomorphic maps from 1-convex domains into ?$q$?-convex manifoldsNaj 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 mnogoterostiTEXTvisokošolska delatheses and dissertationsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza v Ljubljani, Fakulteta za matematiko in fiziko