Some applications of neutrix calculus to composition of distributions

The Composition of distributions is a problem studied from the earliest days of the development of the distribution theory. British mathematician Brian Fisher defined the neutrix composition of distributions using the concept of neutrix limit has been developed by Van Der Corput. In this study, it is intended to show the existence of some distribution of neutrix composition and to calculate compositions of these distributions. The thesis consists of four chapters. In the first and second chapter, entry and test functions space, which is necessary to give the definition of distribution, have been defined and after the distribution space and its some properties have been investigated. In the third chapter, neutrix and neutrix limit concepts have been given with examples. In the last chapter, how to use the concept of the neutrix on the defining of the composition of distributions has been given and then the neutrix composition of distributions x_¯ ̾ lnx_ and x ̟ͬ , x_¯ ̾ ln ͫ x_ and H(x) have been calculated. KeyWords Neutrix, neutrix limit, distribution, composition of neutrix