The compositions derived from by changing variable in singular distributions

Authors

EMİN ÖZÇAĞFollow

Author ORCID Identifier

EMİN ÖZÇAĞ: 0000-0002-4072-1756

DOI

10.55730/1300-0098.3557

Abstract

In this paper we concern further results of \cite{kn:oz9,kn:oz8} by using the method mainly related to the finite part of divergent integral, in fact we consider the powers for positive integers of the composition of the Dirac delta function and an infinitely differentiable function having any number of distinct multiple roots which will be defined as the neutrix limit of the regular sequence $\delta^k_n(f(x))$. Moreover we show that the powers of the composition $\delta(f(x))$ for negative integers can be also defined via neutrix settings. Some compositions as examples to better understand will be given.

Keywords

Divergent integral, regular sequence, Hadamard's finite part, Dirac-delta function, singular distribution, neutrix limit, Fisher's method, Fa´a di Bruno's formulae, cosmology

First Page

1001

Last Page

1023

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Recommended Citation

ÖZÇAĞ, EMİN (2024) "The compositions derived from by changing variable in singular distributions," Turkish Journal of Mathematics: Vol. 48: No. 6, Article 2. https://doi.org/10.55730/1300-0098.3557
Available at: https://journals.tubitak.gov.tr/math/vol48/iss6/2