Generalized Cauchy's Models and Generalized Integrals

Sabra Ramadan

doi:10.3844/jmssp.2007.21.23

Abstract

The space of generalized complex numbers C* has been constructed. The Cachy's model in the space of new generalized functions is well defined. The generalized integral of new generalized function over the compact K has been defined.

Highlights

Antonevich and Radyno[1] gave the following general method of constructing algebras of new generalized functions: Let E- be some generalized function space and there is a some algebra A of infinitely many differentiable functions such that A ⊂ E
Some method of regularization define by a set of linear operators Rψ,ε : E → A, ψ ∈ φ, ε ∈ ς so that ∀ ψ ∈ φ, u ∈ E Rψ,ε (u) → u in since of topology of E
We define the generalized complex numbers correspondence to the space of new generalized functions ζ by the following way: Let G(C) - be the set of all sequences of complex numbers

Summary

Introduction

Antonevich and Radyno[1] gave the following general method of constructing algebras of new generalized functions: Let E- be some generalized function space and there is a some algebra A of infinitely many differentiable functions such that A ⊂ E. We define the generalized complex numbers correspondence to the space of new generalized functions ζ by the following way: Let G(C) - be the set of all sequences of complex numbers.

Results

Conclusion