Babenko-Becknerov teorem

master's thesis

• Author: Ana Perković
• Mentor: Vjekoslav Kovač (mentor)
• Committee member: Vjekoslav Kovač (predsjednik povjerenstva)
• Committee member: Nenad Antonić (član povjerenstva)
• Committee member: Ante Mimica (član povjerenstva)
• Committee member: Ivica Nakić (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2015-07-13, 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: Babenko-Becknerova nejednakost; Fourierova transformacija; Hermiteovi polinomi
• Keywords (english): Babenko-Beckner inequality; Fourier transform; Hermite polynomials
• Language: croatian
• URN:NBN: urn:nbn:hr:217:066505
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-29 12:26:19