dc.contributor.advisor | Grepstad, Sigrid | |
dc.contributor.author | Instanes, Sarah May | |
dc.date.accessioned | 2023-03-25T18:19:24Z | |
dc.date.available | 2023-03-25T18:19:24Z | |
dc.date.issued | 2022 | |
dc.identifier | no.ntnu:inspera:128978531:33898235 | |
dc.identifier.uri | https://hdl.handle.net/11250/3060437 | |
dc.description.abstract | I denne oppgaven studerer vi Riesz-basiser av eksponentialfunksjoner for rommet $L^2(\Omega)$, der $\Omega \subset \bb{R}^d$. Hovedfokuset i oppgaven er å presentere Kozma og Nitzan sitt bevis for at det finnes en Riesz-basis av eksponentialfunksjoner med heltallsfrekvenser i $L^2(\Omega)$ for enhver endelig union av intervaller $\Omega \subset [0,1]$. Vi ser også nærmere på enkelte stabilitets- og tetthetsresultater for eksponentielle Riesz-basiser, og gir detaljerte bevis for Paley--Wieners stabilitetsteorem, Kadec's $\frac{1}{4}$-Teorem og Landaus tetthetsbetingelser for eksponentielle Riesz-basiser. | |
dc.description.abstract | In this thesis we study Riesz bases of exponential functions for spaces $L^2(\Omega)$, where $\Omega \subset \bb{R}^d$. Our main focus will be on proving Kozma and Nitzan's result that given a finite union of intervals $\Omega \subset [0,1]$ we can construct a Riesz basis of exponentials $E(\Lambda)$ with integer frequencies for the space $L^2(\Omega)$. We also study certain stability and density results pertaining to Riesz bases of exponentials, such as the Paley--Wiener stability theorem, Kadec's $\frac{1}{4}$-Theorem, and Landau's necessary density conditions for Riesz bases of exponentials. | |
dc.language | eng | |
dc.publisher | NTNU | |
dc.title | Riesz bases of exponentials for finite unions of intervals | |
dc.type | Master thesis | |