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master's thesis
Uvjetna konvergencija redova
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:576234
Perković, Damjan
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Perković, D. (2020). Uvjetna konvergencija redova (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:576234

Perković, Damjan. "Uvjetna konvergencija redova." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:576234

Perković, Damjan. "Uvjetna konvergencija redova." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:576234

Perković, D. (2020). 'Uvjetna konvergencija redova', Master's thesis, University of Zagreb, Faculty of Science, accessed 08 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:576234

Perković D. Uvjetna konvergencija redova [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 December 08] Available at: https://urn.nsk.hr/urn:nbn:hr:217:576234

D. Perković, "Uvjetna konvergencija redova", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:576234

Metadata
TitleUvjetna konvergencija redova
Title (english)Conditional convergence of rows
AuthorDamjan Perković
MentorTomislav Berić (mentor)
Committee memberTomislav Berić (predsjednik povjerenstva)
Committee memberBoris Širola (član povjerenstva)
Committee memberJosip Tambača (član povjerenstva)
Committee memberAndrej Dujella (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2020-12-01, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu opisuju se pojedina svojstva uvjetno konvergentnih redova u različitim prostorima. U prvom poglavlju bavimo se redovima realnih brojeva te dokazujemo Riemannov teorem, koji pokazuje na koje se načine može promijeniti suma uvjetno konvergentnog reda u R mijenjanjem poretka članova reda. U drugom poglavlju bavimo se redovima vektora u Banachovim prostorima. Na početku poglavlja diskutiraju se odnosi obične, apsolutne i bezuvjetne konvergencije u različitim prostorima. Nadalje, definira se domena sume reda te se dokazuje Steinitzov teorem, koji daje opis domene sume uvjetno konvergentnog reda u konačnodimenzionalnim Banachovim prostorima. Na kraju se diskutira slučaj beskonačnodimenzionalnog prostora i pokazuje se da uvođenjem dodatnih uvjeta Steinitzov teorem vrijedi i u prostorima \(L_p\) , gdje je 1 < p < \(\infty\).
Abstract (english)
In this paper we describe certain properties of conditionally convergent series in different spaces. In the first chapter we deal with series of real numbers and we prove the Riemann series theorem, which shows the ways in which the sum of a conditionally convergent series can be changed by reordering the terms of the series. In the second chapter we deal with series of vectors in Banach spaces. At the beginning of the chapter we discuss the relations between regular, absolute, and unconditional convergence. Furthermore, we define the domain of sums of a series and prove Steinitz’s theorem, which gives a description of the domain of sums of conditionally convergent series in finite-dimensional Banach spaces. In the end we discuss the case of an infinite-dimensional space and we show that, by adding additional conditions to Steinitz’s theorem, it holds in spaces \(L_p\) , where 1 < p < \(\infty\)
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:576234
Study programmeTitle: Mathematical Statistics
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 on2021-02-24 10:30:50