The Fourier series of one class of functions with discontinuities

Abstract

<p>U disertaciji se na bazi redefinisanih pojmova kako prostornog (inte-gralnog) izvoda tako i ostatka (rezidijuma) kompleksnih funkcija defini&scaron;e pojam totalne vrednosti nesvojstvenih integrala. Ova redefinisana vrednost integrala iskori&scaron;ćcena je za dokaz teoreme, koja je uop&scaron;tenje Dirihlejeve teoreme o razvoju realnih funkcija u Furijeov trigonometrijski red.</p>

<p>In this thesis we define the notion of the total value of improper integrals based on the redefined notions of the spatial (integral) derivative and the residue of complex functions. This redefined integrals is used to prove the theorem which is generalization of Dirichlet theorem on the expansion of real valued functions into Fourier trigonometric series.</p>