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master's thesis
Bazni okviri i Rieszove baze Hilbertovih prostora
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:366230
Trgovec, Neven
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Trgovec, N. (2017). Bazni okviri i Rieszove baze Hilbertovih prostora (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:366230

Trgovec, Neven. "Bazni okviri i Rieszove baze Hilbertovih prostora." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:366230

Trgovec, Neven. "Bazni okviri i Rieszove baze Hilbertovih prostora." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:366230

Trgovec, N. (2017). 'Bazni okviri i Rieszove baze Hilbertovih prostora', Master's thesis, University of Zagreb, Faculty of Science, accessed 03 November 2024, https://urn.nsk.hr/urn:nbn:hr:217:366230

Trgovec N. Bazni okviri i Rieszove baze Hilbertovih prostora [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 November 03] Available at: https://urn.nsk.hr/urn:nbn:hr:217:366230

N. Trgovec, "Bazni okviri i Rieszove baze Hilbertovih prostora", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:366230

Metadata
TitleBazni okviri i Rieszove baze Hilbertovih prostora
AuthorNeven Trgovec
MentorDamir Bakić (mentor)
Committee memberDamir Bakić (predsjednik povjerenstva)
Committee memberMarcela Hanzer (član povjerenstva)
Committee memberBojan Basrak (član povjerenstva)
Committee memberIvan Kovač (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-09-26, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovome radu uvodimo pojmove Rieszove baze i baznog okvira u Hilbertovim prostorima te prezentiramo njihova osnovna svojstva i neke karakterizacije. Pritom kao alate koristimo rezultate iz opće teorije normiranih prostora, a koje detaljno navodimo u prvom poglavlju. U glavnom dijelu rada, definiramo približno Rieszove baze te ih, pomoću nekih posebnih vrsta baznih okvira, karakteriziramo, povezujući tako dva osnovna pojma rada. Nadalje, uvodimo pojam viškova baznih okvira koje također detaljno karakteriziramo te analiziramo neka njihova važna svojstva. Pokazuje da se da su bazni okviri s konačnim viškom tada nužno i približno Rieszove baze. Također, duale baznih okvira karakterizirali smo pomoću njihovih viškova.
Abstract (english)
In this thesis, we introduce Riesz bases and frames in Hilbert spaces and we give some of their main properties and characterisations. In doing so, we use results that are a part of general normed spaces theory, which are all stated in the first chapter. In the main part of the thesis, we define near-Riesz bases and give their characterizations in terms of some special types of frames, connecting two main objects of this thesis. Furthermore, we introduce excesses of frames, for which we also give certain characterizations, and we analyse some of their important properties. We show that frames with finite excesses are also near-Riesz bases. Also, we characterize duals of frames in relation to their excesses.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:366230
Study programmeTitle: Finance and Business Mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
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Created on2018-05-04 11:18:22