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master's thesis
Parsevalovi bazni okviri Hilbertovih prostora
Zagreb: University of Zagreb, Faculty of Science, 2018. urn:nbn:hr:217:562271
Grbac, Matko
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Grbac, M. (2018). Parsevalovi bazni okviri Hilbertovih prostora (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:562271

Grbac, Matko. "Parsevalovi bazni okviri Hilbertovih prostora." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:562271

Grbac, Matko. "Parsevalovi bazni okviri Hilbertovih prostora." Master's thesis, University of Zagreb, Faculty of Science, 2018. https://urn.nsk.hr/urn:nbn:hr:217:562271

Grbac, M. (2018). 'Parsevalovi bazni okviri Hilbertovih prostora', Master's thesis, University of Zagreb, Faculty of Science, accessed 16 May 2024, https://urn.nsk.hr/urn:nbn:hr:217:562271

Grbac M. Parsevalovi bazni okviri Hilbertovih prostora [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2018 [cited 2024 May 16] Available at: https://urn.nsk.hr/urn:nbn:hr:217:562271

M. Grbac, "Parsevalovi bazni okviri Hilbertovih prostora", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2018. Available at: https://urn.nsk.hr/urn:nbn:hr:217:562271

Metadata
TitleParsevalovi bazni okviri Hilbertovih prostora
AuthorMatko Grbac
MentorDamir Bakić (mentor)
Committee memberDamir Bakić (predsjednik povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberMatija Kazalicki (član povjerenstva)
Committee memberEduard Marušić-Paloka (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2018-09-24, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu najprije izlažemo neke osnovne pojmove i rezultate iz teorije normiranih prostora koji će se koristiti tijekom daljnjeg proučavanja. Nakon toga uvodimo pojmove Besselovog niza i baznog okvira, pojmove koji će biti središnji dio naših promatranja. Poseban naglasak imaju Parsevalovi bazni okviri. Opisuju se njihova osnovna svojstva te veze između navedenih pojmova. Poseban dio posvećen je dualnim baznim okvirima te njihovoj karakterizaciji pomoću ograničenih operatora koji posjeduju lijevi inverz. Zatim definiramo viškove baznih okvira, navodimo neka svojstva, te naposljetku pomoću istih dolazimo do karakterizacije baznih okvira koji posjeduju Parsevalov dual. Nadalje, opisujemo Besselove nizove koji dopuštaju konačno proširenje do baznog okvira. Za sam kraj rada izlažemo i kratko komentiramo fundamentalnu jednakost za Parsevalove bazne okvire.
Abstract (english)
In this thesis we first give some of the fundamental terms and results from the theory of normed spaces which will be used during further study. Afterwards, we introduce Bessel sequences and frames, terms which will be central part of our study. Special emphasis is put on Parseval frames. We describe their properties and the connections between aforementioned terms. Special part is dedicated to dual frames and their characterization using bounded operators which possess left inverse. Next we define excesses of frames, state some of their properties, and finally give a characterization of frames that possess Parseval dual by using excesses of frames. Furthermore, we describe Bessel sequences that allow finite extension to a frame. In the last part we give a fundamental identity for Parseval frames, as well as a brief discussion considering this identity.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:562271
Study programmeTitle: Pure 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
Terms of useLicence In copyright icon
Created on2019-04-23 10:50:47