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master's thesis
Babenko-Becknerov teorem
Zagreb: University of Zagreb, Faculty of Science, 2015. urn:nbn:hr:217:066505
Perković, Ana
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Perković, A. (2015). Babenko-Becknerov teorem (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:066505

Perković, Ana. "Babenko-Becknerov teorem." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:066505

Perković, Ana. "Babenko-Becknerov teorem." Master's thesis, University of Zagreb, Faculty of Science, 2015. https://urn.nsk.hr/urn:nbn:hr:217:066505

Perković, A. (2015). 'Babenko-Becknerov teorem', Master's thesis, University of Zagreb, Faculty of Science, accessed 07 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:066505

Perković A. Babenko-Becknerov teorem [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2015 [cited 2024 December 07] Available at: https://urn.nsk.hr/urn:nbn:hr:217:066505

A. Perković, "Babenko-Becknerov teorem", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2015. Available at: https://urn.nsk.hr/urn:nbn:hr:217:066505

Metadata
TitleBabenko-Becknerov teorem
AuthorAna Perković
MentorVjekoslav Kovač (mentor)
Committee memberVjekoslav Kovač (predsjednik povjerenstva)
Committee memberNenad Antonić (član povjerenstva)
Committee memberAnte Mimica (član povjerenstva)
Committee memberIvica Nakić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2015-07-13, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
Ovaj rad iznosi osnove Fourierove analize na realnom pravcu, čiji važni koncepti su Fourierova transformacija i Hermiteovi polinomi. Obrazlaže se kako se u realnoj analizi mogu prikladno iskoristiti rezultati iz teorije vjerojatnosti: centralni granični teorem i slaba konvergencija prema Gaussovoj mjeri. U tu svrhu se dokazuju tzv. nejednakost za dvije točke i rezultat za produkt operatora. Pokazuje se veza između simetričnih funkcija i Hermiteovih polinoma. Naposljetku, koristeći iznesene rezultate dokazuje se Babenko-Becknerova nejednakost.
Abstract (english)
This thesis reviews the basic results of the Fourier analysis on the real line, whose important concepts are the Fourier transform and the Hermite polynomials. It elaborates how to apply some results from probability theory to the real analysis: these are the central limit theorem and weak convergence towards the Gaussian measure. With this purpose the so-called two point inequality and result for product of operators are established. The relationship between symmetric functions and Hermite polynomials is also explored. In the end, the Babenko-Beckner inequality is derived from the established results.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:066505
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 on2019-01-29 12:26:19