Decomposition of a Nonlinear Multivariate Function using the Heaviside Step Function
📝 Original Info
- Title: Decomposition of a Nonlinear Multivariate Function using the Heaviside Step Function
- ArXiv ID: 1404.4338
- Date: 2014-05-22
- Authors: Researchers from original ArXiv paper
📝 Abstract
Whereas the Dirac delta function introduced by P. A. M. Dirac in 1930 in his famous quantum mechanics text has been well studied, a not famous formula related to the delta function using the Heaviside step function in a single-variable form, also given in Dirac's text, has been poorly studied. We demonstrate the decomposition of a nonlinear multivariate function into a sum of integrals in which each integrand is composed of a derivative of the function and a direct product of Heaviside step functions. It is an extension of Dirac's single-variable form to that for multiple variables. Moreover, it remains mathematically equivalent to the definition of the Dirac delta function with multiple variables, and offers a mathematically unified expression.💡 Deep Analysis
Deep Dive into Decomposition of a Nonlinear Multivariate Function using the Heaviside Step Function.Whereas the Dirac delta function introduced by P. A. M. Dirac in 1930 in his famous quantum mechanics text has been well studied, a not famous formula related to the delta function using the Heaviside step function in a single-variable form, also given in Dirac’s text, has been poorly studied. We demonstrate the decomposition of a nonlinear multivariate function into a sum of integrals in which each integrand is composed of a derivative of the function and a direct product of Heaviside step functions. It is an extension of Dirac’s single-variable form to that for multiple variables. Moreover, it remains mathematically equivalent to the definition of the Dirac delta function with multiple variables, and offers a mathematically unified expression.