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arXiv · 1404.4338

Decomposition of a Nonlinear Multivariate Function using the Heaviside Step Function

Eisuke Chikayama
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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.

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Eisuke Chikayama. 2014-05-21. Decomposition of a Nonlinear Multivariate Function using the Heaviside Step Function. https://arxiv.org/abs/1404.4338

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