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master's thesis
Spektralna teorija operatora na Hilbertovim prostorima
Split: University of Split, Faculty of Science, 2023. urn:nbn:hr:166:779208
Omazić, Matea
University of Split
Faculty of Science
Department of Mathematics

Institutional repository: Repository of Faculty of Science

Cite this document

Omazić, M. (2023). Spektralna teorija operatora na Hilbertovim prostorima (Master's thesis). Split: University of Split, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:779208

Omazić, Matea. "Spektralna teorija operatora na Hilbertovim prostorima." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:779208

Omazić, Matea. "Spektralna teorija operatora na Hilbertovim prostorima." Master's thesis, University of Split, Faculty of Science, 2023. https://urn.nsk.hr/urn:nbn:hr:166:779208

Omazić, M. (2023). 'Spektralna teorija operatora na Hilbertovim prostorima', Master's thesis, University of Split, Faculty of Science, accessed 07 January 2025, https://urn.nsk.hr/urn:nbn:hr:166:779208

Omazić M. Spektralna teorija operatora na Hilbertovim prostorima [Master's thesis]. Split: University of Split, Faculty of Science; 2023 [cited 2025 January 07] Available at: https://urn.nsk.hr/urn:nbn:hr:166:779208

M. Omazić, "Spektralna teorija operatora na Hilbertovim prostorima", Master's thesis, University of Split, Faculty of Science, Split, 2023. Available at: https://urn.nsk.hr/urn:nbn:hr:166:779208

Metadata
TitleSpektralna teorija operatora na Hilbertovim prostorima
Title (english)Spectral theory of operators on Hilbert spaces
AuthorMatea Omazić
MentorSaša Krešić Jurić (mentor)
Committee memberSaša Krešić Jurić (predsjednik povjerenstva)
Committee memberDino Peran (član povjerenstva)
Committee memberAndrijana Ćurković (član povjerenstva)
GranterUniversity of Split
Faculty of Science
(Department of Mathematics)
Split
Defense date and country2023-05-25, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Rad započinjemo razmatranjem ograničenih operatora na Hilbertovim prostorima, te njihovih spektralnih svojstva. Posebno nas zanimaju sektralne reprezentacije hermitskih i unitranih operatora. Zatim uvodimo pojam neograničenih operatora u Hilbertovim prostorima, te promatramo neke njhove posebne klase. Nakon toga proučavamo spektralna svojstva i spektralnu reprezentaciju neograničenih operatora. Posebno promatramo svojstva operatora množenja i deriviranja na \(L^{2}\)(\({- \infty }, {+\infty }\)). Ove objekte i njihova svojstva proučavamo unutar teorije Hilbertovih operatora, te kada je potrebno koristimo poznate teoreme iz teorije mjere.
Abstract (english)
We start the theses by considering bounded operators on Hilbert spaces, as well as their spectral properties. We examine in detail spectral representations of self-adjoint and unitary operators. We Then introduce unbounded operators in Hilbert spaces and analyze some special classes of these operators. We also study spectral properties and spectral representations of unbounded operators, as well as the properties of multiplication and differentiation operators on \(L^{2}\)(\({- \infty }, {+\infty }\)). We study these objects within the theory of Hilbert spaces, using standard theorems from measure theory when neccesary.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:779208
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in pure mathematics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2023-06-02 09:30:22