{"?xml":{"@version":"1.0"},"edm:RDF":{"@xmlns:dc":"http://purl.org/dc/elements/1.1/","@xmlns:edm":"http://www.europeana.eu/schemas/edm/","@xmlns:wgs84_pos":"http://www.w3.org/2003/01/geo/wgs84_pos","@xmlns:foaf":"http://xmlns.com/foaf/0.1/","@xmlns:rdaGr2":"http://rdvocab.info/ElementsGr2","@xmlns:oai":"http://www.openarchives.org/OAI/2.0/","@xmlns:owl":"http://www.w3.org/2002/07/owl#","@xmlns:rdf":"http://www.w3.org/1999/02/22-rdf-syntax-ns#","@xmlns:ore":"http://www.openarchives.org/ore/terms/","@xmlns:skos":"http://www.w3.org/2004/02/skos/core#","@xmlns:dcterms":"http://purl.org/dc/terms/","edm:WebResource":[{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-6JRT32HO/29065a63-727b-4647-a9e6-eb714b387541/HTML","dcterms:extent":"162 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-6JRT32HO/9008ea54-198e-4edf-8bd5-85e234072ba8/PDF","dcterms:extent":"8067 KB"},{"@rdf:about":"http://www.dlib.si/stream/URN:NBN:SI:DOC-6JRT32HO/9ae9274a-1bf8-4358-bc06-4b2732be561d/TEXT","dcterms:extent":"80 KB"}],"edm:ProvidedCHO":{"@rdf:about":"URN:NBN:SI:DOC-6JRT32HO","dcterms:issued":"2008","dc:creator":"Globevnik, Josip","dc:contributor":"Vidav, Ivan","dc:format":{"@xml:lang":"sl","#text":"63 strani"},"dc:identifier":["COBISSID:238961408","URN:URN:NBN:SI:doc-6JRT32HO"],"dc:language":"sl","dc:publisher":[{"@xml:lang":"sl","#text":"dLib distributer"},{"@xml:lang":"sl","#text":"J. Globevnik"}],"dc:source":{"@xml:lang":"sl","#text":"visokošolska dela"},"dc:subject":[{"@xml:lang":"sl","#text":"analitične funkcije s konstantno normo"},{"@xml:lang":"en","#text":"complex analysisu"},{"@xml:lang":"sl","#text":"kompleksna analiza"},{"@xml:lang":"sl","#text":"vektorske analitične funkcije"}],"dc:title":{"@xml:lang":"sl","#text":"Analitične funkcije s konstantno normo| doktorska disertacija|"},"dc:description":[{"@xml:lang":"sl","#text":"A complex-valued analytic function ?$f$?, defined on a domain ?$D$? in the complex plane, satisfying ?$\\|f(\\zeta)\\|=1$? ?$(\\zeta \\in D)$? is necessarily a constant. In general this is no longer true if the function has values in a complex Banach space. We study analytic functions from ?$D$? into a complex Banach space whose norm is constant on ?$D$?. Various necessary and sufficient conditions are obtained to assure that a nonconstant analytic function from ?$D$? to a complex Banach space has constant norm on ?$D$?. We study also the analytic functions ?$f$? from ?$D$? to a complex Banach space having the following property: there exist a complex-valued analytic function ?$\\varphi$? on ?$D$? such that ?$\\|f(z)\\|=|\\varphi(z)|$? ?$(z\\inD)$?"},{"@xml:lang":"sl","#text":"Če za kompleksno analitično funkcijo ?$f$?, definirano na polju ?$D$? v kompleksni ravnini, velja ?$\\|f(\\zeta)\\|=1$? ?$(\\zeta \\in D)$?, tedaj je ?$f$? konstanta. To ne velja v splošnem za funkcije z vrednostmi v kompleksnem Banachovem prostoru. Proučujemo analitične funkcije na ?$D$? z vrednostmi v kompleksnem Banachovem prostoru, za katere je ?$\\|f(\\zeta)\\|=1$? ?$(\\zeta \\in D)$?. Dobljeni so različni potrebni in zadostni pogoji za to, da ima nekonstantna analitična funkcija na ?$D$? konstantno normo. Študirane so tudi analitične funkcije ?$f$? na ?$D$? z vrednostmi v kompleksnem Banachovem prostoru, za kater obstaja skalarna analitična funkcija ?$\\varphi$? na ?$D$?, da velja ?$\\|f(z)\\| = |\\varphi(z)|$? ?$(z \\in D)$?"},{"@xml:lang":"sl","#text":"doktorska disertacija"}],"edm:type":"TEXT","dc:type":[{"@xml:lang":"sl","#text":"visokošolska dela"},{"@xml:lang":"en","#text":"theses and dissertations"},{"@rdf:resource":"http://www.wikidata.org/entity/Q1266946"}]},"ore:Aggregation":{"@rdf:about":"http://www.dlib.si/?URN=URN:NBN:SI:DOC-6JRT32HO","edm:aggregatedCHO":{"@rdf:resource":"URN:NBN:SI:DOC-6JRT32HO"},"edm:isShownBy":{"@rdf:resource":"http://www.dlib.si/stream/URN:NBN:SI:DOC-6JRT32HO/9008ea54-198e-4edf-8bd5-85e234072ba8/PDF"},"edm:rights":{"@rdf:resource":"http://rightsstatements.org/vocab/InC/1.0/"},"edm:provider":"Slovenian National E-content Aggregator","edm:intermediateProvider":{"@xml:lang":"en","#text":"National and University Library of Slovenia"},"edm:dataProvider":{"@xml:lang":"sl","#text":"Univerza v Ljubljani, Fakulteta za matematiko in fiziko"},"edm:object":{"@rdf:resource":"http://www.dlib.si/streamdb/URN:NBN:SI:DOC-6JRT32HO/maxi/edm"},"edm:isShownAt":{"@rdf:resource":"http://www.dlib.si/details/URN:NBN:SI:DOC-6JRT32HO"}}}}