Hilbertov prostor

master's thesis

• Author: Maja Štajduhar
• Mentor: Zvonko Iljazović (mentor)
• Committee member: Zvonko Iljazović (predsjednik povjerenstva)
• Committee member: Mirko Primc (član povjerenstva)
• Committee member: Boris Guljaš (član povjerenstva)
• Committee member: Dražen Adamović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2016-07-13, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu, u prvom poglavlju objasnili smo neke osnovne činjenice vezane uz vektorski i metrički prostor. Proučili smo konvergentne nizove i redove. U drugom poglavlju definirali smo Hilbertov prostor te povezujući elementarna svojstva iz prvog poglavlja ispitali smo od kakvih nizova se on sastoji. Dokazali smo da je Hilbertov prostor potprostor vektorskog prostora, da je separabilan i potpun te smo dokazali da je strogo konveksan bez grananja.

Abstract (english)

In this thesis in the first chapter, we explained some basic facts related to the vector and metric spaces. We also examined convergent sequences and series. In the second chapter we defined the Hilbert space and linking the basic properties of the first chapter we examined from which series he is composed. We proved that the Hilbert space is a subspace of vector space, that is separable and complete, and we also proved that it is strongly convex without ramifications.

• Keywords: Hilbertov prostor; konvergentni redovi; konvergentni nizovi
• Keywords (english): Hilbert space; convergent sequences; convergent series
• Language: croatian
• URN:NBN: urn:nbn:hr:217:478477
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-02-14 09:18:13