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master's thesis
Fourierova transformacija i Paley-Wienerov prostor
Zagreb: University of Zagreb, Faculty of Science, 2017. urn:nbn:hr:217:862953
Kovačević, Antonija
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

Cite this document

Kovačević, A. (2017). Fourierova transformacija i Paley-Wienerov prostor (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:862953

Kovačević, Antonija. "Fourierova transformacija i Paley-Wienerov prostor." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:862953

Kovačević, Antonija. "Fourierova transformacija i Paley-Wienerov prostor." Master's thesis, University of Zagreb, Faculty of Science, 2017. https://urn.nsk.hr/urn:nbn:hr:217:862953

Kovačević, A. (2017). 'Fourierova transformacija i Paley-Wienerov prostor', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:862953

Kovačević A. Fourierova transformacija i Paley-Wienerov prostor [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2017 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:862953

A. Kovačević, "Fourierova transformacija i Paley-Wienerov prostor", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:217:862953

Metadata
TitleFourierova transformacija i Paley-Wienerov prostor
AuthorAntonija Kovačević
MentorDamir Bakić (mentor)
Committee memberDamir Bakić (predsjednik povjerenstva)
Committee memberZoran Vondraček (član povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberPavle Goldstein (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2017-11-28, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovome radu izložene su osnove Fourierove transformacije na Banachovom prostoru \(L^1(\mathbb{R})\) i Hilbertovom prostoru \(L^2(\mathbb{R})\). Također, opisana su glavna svojstva Paley-Wienerovog prostora i dokazan je teorem o uzorkovanju na tom prostoru. Rad je podijeljen u četiri idejne cjeline, u prvom poglavlju navedeni su rezultati iz teorije normiranih prostora, te mjere i integrala koji su potrebni u proučavanju Fourierove transformacije. U drugome dijelu pažnju smo posvetili baznim okvirima koji se pokazuju korisnima u samom teoremu o uzorkovanju. Treće poglavlje posvećeno je Fourierovoj transformaciji. U četvrtom poglavlju uvodi se Paley-Wienerov prostor, proučavaju se svojstva tog prostora i na samom kraju, dokaže se teorem o uzorkovanju.
Abstract (english)
In this thesis we introduce outlines of Fourier transform in Banach space \(L^1(\mathbb{R})\) and Hilbert space \(L^2(\mathbb{R})\). Also, main properties of Paley-Wiener space is disscused and Sampling theorem has been proved. The thesis consists of four parts. Chapter 1 is a review of normed linear spaces theory and measure and integration theory, needed in coming chapters. Chapter 2 is devoted to frames, which will show useful in the Sampling theorem. In Chapter 3 we commit to Fourier transform. In final chapter, Paley-Wiener space has been introduced, main properties have been brought up and Classical Sampling Theorem has been demonstrated.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:862953
Study programmeTitle: Applied 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 on2018-05-25 11:59:45