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New Horizons in Mathematical Physics
NHMP > Volume 4, Number 1, March 2020

Quantum Integration Using Dirac’s Delta Function

Download PDF  (611.5 KB)PP. 1-13,  Pub. Date:March 16, 2020
DOI: 10.22606/nhmp.2020.41001

Author(s)
Reza Ahangar
Affiliation(s)
Department of Mathematics, Texas A & M University - Kingsville, United States
Abstract
A historical review of Dirac’s Delta functions is presented. It is developed as a generalized function in the space Bochner-Lebesgue summable function. Further properties of the absolute, asymptotic continuity, and differentiability of Bochner summable functions is also investigated. We can generalize the equivalent of Bochner-Stieltjes summability and absolute continuity, asymptotic continuity, and differentiability. Dirac Delta sequence of functions will be presented as a generalized function with a convolution operator where we use it as a charaterization of compactness in the space of Bochner summable functions. We will propose a perturbed differential equation such that the perturbation function is a sequence Dirac’s Delta function which is a Bochner summable function.
Keywords
Lebesgue Bochner integration, Dirac’s Delta function, Compact Operators, Space of Summable Functions, Absolute and Asymptotic Continuity and Differentiability, Nonlinear Operator Differential Equations, impulsive perturbation.
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