Unit:
Κατεύθυνση Εφαρμοσμένα ΜαθηματικάLibrary of the School of Science
Supervisors info:
Ανθίππη Πούλκου Επίκ.Καθηγήτρια ΕΚΠΑ (Επιβλέπουσα), Ιωάννης Στρατής Καθηγητής ΕΚΠΑ, Ευαγγελία Αθανασιάδου-Κόττα Λέκτορας ΕΚΠΑ
Original Title:
Aκολουθιακή θεωρία γενικευμένων συναρτήσεων
Translated title:
Sequential theory of generalized functions
Summary:
In this Thesis we demonstrate the basic calculus definitions and theorems.
Then, we thoroughly present fundamental concepts and results of generalized
functions. Moreover, we examine the integral transforms using generalized
functions, we study the Fourier integrals and we generalize the study of
integral transforms. Later on, we examine the weak integration with its
generalized form and we apply the results by changing the variable in a weak
function. Finally, we introduce the concept of asymptoticism, we study the
behavior of initial function in their critical points, we examine the
asymptotic behavior of Fourier Integrals and we showcase some of the
applications of the above-mentioned concepts.
Keywords:
Generalized functions, Weak functions, Fourier-type of integrals, Asymptotic functions, Weak integration
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