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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   Faculty/Department--Faculty of Sciences and Engineering--Department of Mathematics and Applied Mathematics--Post-graduate theses
  Type of Work--Post-graduate theses
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