{"id":{"repo_id":"oldenburg","oai_identifier":"oai:oops.uni-oldenburg.de:91"},"canonical_url":"https://search.dev.ndltd.org/etd/oldenburg/oai:oops.uni-oldenburg.de:91","repository":{"repo_id":"oldenburg","name":"Carl von Ossietzky Universität Oldenburg","base_url":"http://oops.uni-oldenburg.de/cgi/oai2"},"display":{"title":"Domains of convergence in infinite dimensional holomorphy","abstract":"For certain subsets F(R) of holomorphic functions on a Reinhardt domain R in a Banach sequence space X, mainly for H_{\\infty}(R), P^m(X) and P(X), we give precise descriptions of the domain of convergence dom F(R), i.e. the set of all points of R where the monomial expansion \\sum_{\\alpha\\in \\N_0^{(\\N)}} \\frac{\\partial^{\\alpha} f (0)}{\\alpha !} z^{\\alpha} of every function f \\in F(R) is (unconditionally) convergent. The results are obtained by an interplay of complex analysis and local Banach space theory, improving work of Ryan and Lempert about monomial expansions of holomorphic functions on \\ell_1 and using methods from the theory of multidimensional Bohr radii. The problem of conditional convergence is solved for polynomials. It is closely connected with bases for full and symmetric tensor products and convergence preserving permutations.","abstract_html":"For certain subsets F(R) of holomorphic functions on a Reinhardt domain R in a Banach sequence space X, mainly for H_{\\infty}(R), P^m(X) and P(X), we give precise descriptions of the domain of convergence dom F(R), i.e. the set of all points of R where the monomial expansion \\sum_{\\alpha\\in \\N_0^{(\\N)}} \\frac{\\partial^{\\alpha} f (0)}{\\alpha !} z^{\\alpha} of every function f \\in F(R) is (unconditionally) convergent. The results are obtained by an interplay of complex analysis and local Banach space theory, improving work of Ryan and Lempert about monomial expansions of holomorphic functions on \\ell_1 and using methods from the theory of multidimensional Bohr radii. The problem of conditional convergence is solved for polynomials. It is closely connected with bases for full and symmetric tensor products and convergence preserving permutations.","abstract_has_math":false,"creators":["Prengel, Christopher"],"institution":"Universität Oldenburg","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":[],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2005,"date_issued":"2005-10-26","date_published":"2005-10-26","updated_at":"2026-07-27T20:27:08Z","subjects":["[Keine Schlagwörter von Autor/in vergeben.]"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://oops.uni-oldenburg.de/91","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:creator","label":"Author","values":["Prengel, Christopher"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["BIS der Universität Oldenburg"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Oldenburg"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["[Keine Schlagwörter von Autor/in vergeben.]"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["For certain subsets F(R) of holomorphic functions on a Reinhardt domain R in a Banach sequence space X, mainly for H_{\\infty}(R), P^m(X) and P(X), we give precise descriptions of the domain of convergence dom F(R), i.e. the set of all points of R where the monomial expansion \\sum_{\\alpha\\in \\N_0^{(\\N)}} \\frac{\\partial^{\\alpha} f (0)}{\\alpha !} z^{\\alpha} of every function f \\in F(R) is (unconditionally) convergent. The results are obtained by an interplay of complex analysis and local Banach space theory, improving work of Ryan and Lempert about monomial expansions of holomorphic functions on \\ell_1 and using methods from the theory of multidimensional Bohr radii. The problem of conditional convergence is solved for polynomials. It is closely connected with bases for full and symmetric tensor products and convergence preserving permutations.","Für gewisse Teilmengen F(R) holomorpher Funktionen auf einem Reinhardtgebiet R in einem Banachfolgenraum X, vor allem für H_{\\infty}(R), P^m(X) und P(X), geben wir eine genaue Beschreibung des Konvergenzbereichs dom F(R), d.h. der Menge aller Punkte aus R, in denen die Monomialentwicklung \\sum_{\\alpha\\in \\N_0^{(\\N)}} \\frac{\\partial^{\\alpha} f (0)}{\\alpha !} z^{\\alpha} einer jeden Funktion f \\in F(R) (unbedingt) konvergiert. Die Resultate werden durch ein Zusammenspiel von komplexer Analysis und lokaler Banachraumtheorie erzielt, setzen Arbeiten von Ryan und Lempert über Monomialentwicklungen holomorpher Funktionen auf \\ell_1 fort und bedienen sich der Theorie mehrdimensionaler Bohrradien. Das Problem bedingter Konvergenz wird für Polynome gelöst. Es ist eng verknüpft mit Basen für volle und symmetrische Tensorprodukte und konvergenzerhaltenden Permutationen."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Domains of convergence in infinite dimensional holomorphy"]}]}],"canonical_facts":{"dc:creator":["Prengel, Christopher"],"dc:description.abstract":["For certain subsets F(R) of holomorphic functions on a Reinhardt domain R in a Banach sequence space X, mainly for H_{\\infty}(R), P^m(X) and P(X), we give precise descriptions of the domain of convergence dom F(R), i.e. the set of all points of R where the monomial expansion \\sum_{\\alpha\\in \\N_0^{(\\N)}} \\frac{\\partial^{\\alpha} f (0)}{\\alpha !} z^{\\alpha} of every function f \\in F(R) is (unconditionally) convergent. The results are obtained by an interplay of complex analysis and local Banach space theory, improving work of Ryan and Lempert about monomial expansions of holomorphic functions on \\ell_1 and using methods from the theory of multidimensional Bohr radii. The problem of conditional convergence is solved for polynomials. It is closely connected with bases for full and symmetric tensor products and convergence preserving permutations.","Für gewisse Teilmengen F(R) holomorpher Funktionen auf einem Reinhardtgebiet R in einem Banachfolgenraum X, vor allem für H_{\\infty}(R), P^m(X) und P(X), geben wir eine genaue Beschreibung des Konvergenzbereichs dom F(R), d.h. der Menge aller Punkte aus R, in denen die Monomialentwicklung \\sum_{\\alpha\\in \\N_0^{(\\N)}} \\frac{\\partial^{\\alpha} f (0)}{\\alpha !} z^{\\alpha} einer jeden Funktion f \\in F(R) (unbedingt) konvergiert. Die Resultate werden durch ein Zusammenspiel von komplexer Analysis und lokaler Banachraumtheorie erzielt, setzen Arbeiten von Ryan und Lempert über Monomialentwicklungen holomorpher Funktionen auf \\ell_1 fort und bedienen sich der Theorie mehrdimensionaler Bohrradien. Das Problem bedingter Konvergenz wird für Polynome gelöst. Es ist eng verknüpft mit Basen für volle und symmetrische Tensorprodukte und konvergenzerhaltenden Permutationen."],"dc:format.medium":["application/pdf"],"dc:publisher":["BIS der Universität Oldenburg"],"dc:subject":["[Keine Schlagwörter von Autor/in vergeben.]"],"dc:title":["Domains of convergence in infinite dimensional holomorphy"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Oldenburg"]},"updated_at":"2026-07-27T20:27:08Z"}