title: Decomposition of multivariate function using the Heaviside step function.
abstract: Whereas the Dirac delta function introduced by P. A. M. Dirac in 1930 to develop his theory of quantum mechanics 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 by Dirac, has been poorly studied. Following Dirac's method, we demonstrate the decomposition of a 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.
authors.affiliation: Department of Information Systems, Niigata University of International and Information Studies, 3-1-1 Mizukino, Nishi-ku, Niigata-shi, Niigata, 950-2292 Japan ; Environmental Metabolic Analysis Research Team, RIKEN, 1-7-22 Suehiro-cho, Tsurumi-ku, Yokohama-shi, Kanagawa, 230-0045 Japan ; Image Processing Research Team, RIKEN, 2-1 Hirosawa, Wako-shi, Saitama, 351-0198 Japan.
authors.forename: Eisuke
authors.initials: E
authors.lastname: Chikayama
keywords: Dirac delta function; Heaviside step function; Transform