New Horizons in Mathematical Physics

Download PDF (611.5 KB) PP. 1 - 13 Pub. Date: March 17, 2020

DOI: 10.22606/nhmp.2020.41001

• Reza Ahangar^*
  Department of Mathematics, Texas A & M University - Kingsville, United States

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.

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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