Abstract

The space of new Generalized functions ζ (Π(R)) has been constructed. The operation of associative multiplication Θ has been defined on ζ (Π(R)).The embedding Jπ : ζ(S(R))→ ζ( (R)) has been constructed.

Highlights

  • One of the first problems in distributions theory is how to define the associative multiplication in distribution spaces S/ and D /

  • Colomboea J.E.[2] and his contemporaries studied the algebra of the objects referred to as "New Generalized Functions"

  • By T(E) we denote the set of all possible sequences in E, where E be separated locally -convex algebra with topology defined by family of semi norms (Pα )α∈A such that for α ∈ A, there exist β ∈ A a constant Cα > o for which ρα (λ.γ) ≤ Cα Pβ (λ) Pβ (γ) ∀ λ, γ ∈ E

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Summary

Introduction

One of the first problems in distributions theory is how to define the associative multiplication in distribution spaces S/ and D /. Abstract: The space of new Generalized functionsζ (∏(R)) has been constructed. The operation of associative multiplication Θ has been defined on ζ (∏(R)) .The embedding Jπ :ζ (S(R)) → ζ(∏(R)) Schwartz(1) demonstrated the impossibility to define Associative Multiplication in such spaces.

Results
Conclusion

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