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

Journal Article · Sun Sep 01 04:00:00 EDT 1996 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.531649· OSTI ID:286931

Lenglart, E ^[1]; Gouesbet, G ^[2]

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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)

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.}

• OSTI ID: 286931
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 9 Vol. 37; ISSN JMAPAQ; ISSN 0022-2488
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
99 GENERAL AND MISCELLANEOUS
COORDINATES
CYLINDRICAL CONFIGURATION
ELECTROMAGNETIC FIELDS
FUNCTIONAL ANALYSIS
LIGHT SCATTERING
PARTIAL DIFFERENTIAL EQUATIONS
WAVE EQUATIONS