Bazı Singular Genelleştirilmiş Fonksiyonların Neutrix Kompozisyonları

Abstract

In this thesis by using the neutrix calculus, the neutrix compositions of some special generalized functions are defined.The thesis consists of five chapters.The first chapter is an introduction to the thesis. In the second chapter, the definitions of generalized function with their some properties and the concepts of neutrix, neutrix limit with examples, also the concept of compositions of generalized functions are given. In the third chapter, the neutrix composition (x+r)-s of the generalized functions x-s and x+r is defined.In the fourth chapter, the meaning was given to the negative powers of Heaviside generalized function H(x) . Also, at the end of chapter the neutrix compositions [H(x)]--s and [H(x)]+-s are defined.In the last chapter, let µϵR+ , m=1,2,… such that µmϵZ+. Then the neutrix composition (x+µ)-m of x+µ and x-m is defined.