Potpuno razgranati konačni bazni okviri

master's thesis

• Author: Anda Rabatić
• Mentor: Damir Bakić (mentor)
• Committee member: Damir Bakić (predsjednik povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Committee member: Matija Bašić (član povjerenstva)
• Committee member: Goran Muić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2019-10-10, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

Ovaj je rad izložio neke od osnovnih rezultata o baznim okvirima na separabilnim Hilbertovim prostorima, pri čemu smo se oslanjali na već poznate činjenice iz linearne algebre i normiranih prostora. Pritom smo posebnu pažnju posvetili konačnim baznim okvirima, koji su u praksi najčešće korišteni. Glavni je dio rada posvećen potpuno razgranatim konačnim baznim okvirima, koji su posebno važni radi svoje maksimalne otpornosti na gubitke informacija prilikom prijenosa podataka. Opisali smo dva... More načina konstrukcije takvih konačnih baznih okvira. Jedan od njih je utemeljen na teoremu Chebotarëva, dok drugi koristi svojstva totalno nesingularnih matrica. Opisali smo i jednu metodu konstrukcije beskonačnih totalno pozitivnih matrica. Less

Abstract (english)

In this thesis we have presented some of the crucial results about frames in separabile Hilbert spaces, whereby we had relied on some well known facts from linear algebra and normed spaces. We paid special attention to finite frames, since they are the ones that are most commonly used in practice. The main part of this thesis is dedicated to finite full spark frames which are especially important due to their maximal robustness to erasures of informations during data transmissions. We... More have described two ways of constructing such frames. One of them is based on Chebotarev's theorem, while the other one uses the properties of totally non-singular matrices. We have also described a particular method of construction of infinite totally positive matrices. Less

• Keywords: bazni okviri; separabilni Hilbertovi prostori; linearna algebra; normirani prostori; teorem Chebotarëva
• Keywords (english): frames; separabile Hilbert spaces; linear algebra; normed spaces; Chebotarev's theorem
• Language: croatian
• URN:NBN: urn:nbn:hr:217:880012
• Study programme: Title: Applied Mathematics; 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: 2020-02-18 11:43:23