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Identifier

000430642

Title

Το πρόβλημα του περιορισμού του μετασχηματισμού Fourier

Alternative Title

The restriction problem of the fourier transform

Author

Φραγκιαδάκη, Βαλέντια

Thesis advisor

Παπαδημητράκης, Μιχάλης

Abstract

In this thesis we will prove the Tomas - Stein theorem for q > and the fact that the range condition for q is the best possible. In particular, the theorem says that if f Ε L2(Sn-1), then fdaq < Cqf L2(sn-i), for every q > ^_+12. The result of the theorem for q = 2n+2 requires different techniques and can not be proven this way. However, the respective problem for f Ε L°°(Sn-1), namely the restriction conjecture of Stein which says that for f Ε L°°(Sn-1) and q > we have fdaq < Cqf is still an open problem. We will only prove that this range of q is the best possible. We begin in Chapter 1 with stating some basic but important facts of the Fourier transform which will be needed later. In Chapter 2, we develop the Stationary Phase method which is useful in computing the Fourier transform of measures with support on submanifolds of Rn, like the sphere Sn-1 which we will need. Finally, in chapter 3, we state and prove the main results of Tomas and Stein.

Language

Greek, English

Subject

Non- strationary phase

Stationary phase method

Μέθοδος στάσιμης φάσης

Μετασχηματισμός Fourier

Πρόβλημα περιορισμού

Issue date

2020-07-24

Collection

School/Department--School of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses