Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Supervisors info:
Δημήτριος Γατζούρας, Καθηγητής, Τμήμα Μαθηματικών, Σχολή Θετικών Επιστημών
Απόστολος Γιαννόπουλος, Καθηγητής, Τμήμα Μαθηματικών, Σχολή Θετικών Επιστημών
Ελευθέριος Κυρούσης, Καθηγητής, Τμήμα Μαθηματικών, Σχολή Θετικών Επιστημών
Original Title:
Ο Μετασχηματισμός Fourier στην ευθεία και τον κύκλο
Translated title:
Fourier Transform in real line and circle
Summary:
In the current thesis we shall talk about issues of series and Fourier Transforms. Firstly, we will see basic results about summability and Fourier series in L^2(T), but also about smoothness conditions that a function must satisfy so that we come to conclusions about the order of magnitude of Fourier coefficients. Particularly, we will study Fourier Analysis through homogeneous Banach spaces. In the end, we will present important results about both Fourier Transform in L^p(R), 1<=p<=2, and Fourier-Stieltjes Transform. This thesis has been based upon selected chapters of Yitzhak's Katznelson book "An Introduction to Harmonic Analysis, Third Corrected Edition".
Main subject category:
Science
Keywords:
Fourier Transform, Fourier coefficients, Fourier-Stieltjes Transform, Homogeneous Banach Space, Convergence
