Rieszove baze i bazni okviri Hilbertovih prostora

master's thesis

• Title (english): Riesz bases and base frames of Hilbert spaces
• Author: Marta Han
• Mentor: Damir Bakić (mentor)
• Committee member: Damir Bakić (predsjednik povjerenstva)
• Committee member: Franka Miriam Brückler (član povjerenstva)
• Committee member: Ana Prlić (član povjerenstva)
• Committee member: Vanja Wagner (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2021-09-23, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Cilj rada bio je uvesti i obraditi osnovne pojmove teorije baznih okvira i otkriti poveznice između posebnih vrsta baznih okvira (egzaktan, Parsevalov,...) s pojmom Rieszove baze te pojmom približno Rieszove baze. Najvažnijim rezultatom završnog poglavlja dobili smo poveznicu približno Rieszove baze s beselskim i bezuvjetnim baznim okvirima. Kako bi bilo moguće ostvariti ovaj cilj uz minimalnu količinu nejasnih i (u radu) nedokazanih tvrdnji, prvo smo morali utvrditi teoriju normiranih prostora i izvesti svojstva Rieszovih baza i Besselovih nizova.

Abstract (english)

The aim of this thesis was to introduce frames and some results of the frame theory in order to find the link between special types of frames - exact and Parseval - and Riesz bases, but also between near-Riesz bases and Besselian and unconditional frames. This was achieved through the main theorems of chapters 2 and 3. In order to accomplish this and avoid relying on results not shown in the thesis as much as possible, it was necessary to start with laying the foundation by revising the theory of normed spaces and deriving the properties of Riesz bases and Bessel sequences. The theory on normed spaces mostly relies on the results in [1] and results about frames can be found in [2].

• Keywords: teorija baznih okvira; približno Rieszove baze; teorija normiranih prostora; Besselovi nizovi
• Keywords (english): frame theory; near-Riesz bases; theory of normed spaces; Bessel sequences
• Language: croatian
• URN:NBN: urn:nbn:hr:217:943316
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2021-10-27 10:57:45