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Title: The separability {open_quote}{open_quote}theorem{close_quote}{close_quote} in terms of distributions with discussion of electromagnetic scattering theory

Abstract

The separability theorem states that, given a linear partial differential equation and special coordinates allowing to find a family of separated solutions, all solutions of physical interest of the equations can be obtained from linear combinations of the separated solutions. In developing the theory of interaction between an infinite cylinder and a Gaussian beam, it has been recently observed that the theorem may fail in terms of functions. In this paper, it is shown that the separability theorem is recovered if solutions are expressed in terms of distributions instead of in terms of functions. Relevance to light scattering theory is discussed. {copyright} {ital 1996 American Institute of Physics.}

Authors:
 [1];  [2]
  1. Laboratoire de Mathematique, Insa de Rouen, B.P. 08, 76131 Mont Saint Aignan Cedex (France)
  2. Laboratoire d`Energetique des Systemes et Procedes, Insa de Rouen, URA CNRS 230, B.P. 08, 76131 Mont Saint Aignan Cedex (France)
Publication Date:
OSTI Identifier:
286931
Resource Type:
Journal Article
Journal Name:
Journal of Mathematical Physics
Additional Journal Information:
Journal Volume: 37; Journal Issue: 9; Other Information: PBD: Sep 1996
Country of Publication:
United States
Language:
English
Subject:
66 PHYSICS; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; LIGHT SCATTERING; PARTIAL DIFFERENTIAL EQUATIONS; FUNCTIONAL ANALYSIS; ELECTROMAGNETIC FIELDS; CYLINDRICAL CONFIGURATION; COORDINATES; WAVE EQUATIONS

Citation Formats

Lenglart, E, and Gouesbet, G. The separability {open_quote}{open_quote}theorem{close_quote}{close_quote} in terms of distributions with discussion of electromagnetic scattering theory. United States: N. p., 1996. Web. doi:10.1063/1.531649.
Lenglart, E, & Gouesbet, G. The separability {open_quote}{open_quote}theorem{close_quote}{close_quote} in terms of distributions with discussion of electromagnetic scattering theory. United States. https://doi.org/10.1063/1.531649
Lenglart, E, and Gouesbet, G. 1996. "The separability {open_quote}{open_quote}theorem{close_quote}{close_quote} in terms of distributions with discussion of electromagnetic scattering theory". United States. https://doi.org/10.1063/1.531649.
@article{osti_286931,
title = {The separability {open_quote}{open_quote}theorem{close_quote}{close_quote} in terms of distributions with discussion of electromagnetic scattering theory},
author = {Lenglart, E and Gouesbet, G},
abstractNote = {The separability theorem states that, given a linear partial differential equation and special coordinates allowing to find a family of separated solutions, all solutions of physical interest of the equations can be obtained from linear combinations of the separated solutions. In developing the theory of interaction between an infinite cylinder and a Gaussian beam, it has been recently observed that the theorem may fail in terms of functions. In this paper, it is shown that the separability theorem is recovered if solutions are expressed in terms of distributions instead of in terms of functions. Relevance to light scattering theory is discussed. {copyright} {ital 1996 American Institute of Physics.}},
doi = {10.1063/1.531649},
url = {https://www.osti.gov/biblio/286931}, journal = {Journal of Mathematical Physics},
number = 9,
volume = 37,
place = {United States},
year = {Sun Sep 01 00:00:00 EDT 1996},
month = {Sun Sep 01 00:00:00 EDT 1996}
}