Decomposition of multivariate function using the Heaviside step function
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. Follow...
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| Format: | Online |
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Springer International Publishing
2014
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| Online Access: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4447849/ |
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pubmed-44478492015-06-01 Decomposition of multivariate function using the Heaviside step function Chikayama, Eisuke Research 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. Springer International Publishing 2014-11-29 /pmc/articles/PMC4447849/ /pubmed/26034693 http://dx.doi.org/10.1186/2193-1801-3-704 Text en © Chikayama; licensee Springer. 2014 This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. |
| repository_type |
Open Access Journal |
| institution_category |
Foreign Institution |
| institution |
US National Center for Biotechnology Information |
| building |
NCBI PubMed |
| collection |
Online Access |
| language |
English |
| format |
Online |
| author |
Chikayama, Eisuke |
| spellingShingle |
Chikayama, Eisuke Decomposition of multivariate function using the Heaviside step function |
| author_facet |
Chikayama, Eisuke |
| author_sort |
Chikayama, Eisuke |
| title |
Decomposition of multivariate function using the Heaviside step function |
| title_short |
Decomposition of multivariate function using the Heaviside step function |
| title_full |
Decomposition of multivariate function using the Heaviside step function |
| title_fullStr |
Decomposition of multivariate function using the Heaviside step function |
| title_full_unstemmed |
Decomposition of multivariate function using the Heaviside step function |
| title_sort |
decomposition of multivariate function using the heaviside step function |
| description |
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. |
| publisher |
Springer International Publishing |
| publishDate |
2014 |
| url |
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4447849/ |
| _version_ |
1613229045779005440 |