Ricardo Estrada and S A Fulling 2002 J. Phys. A: Math. Gen. 35 3079 doi:10.1088/0305-4470/35/13/304
Ricardo Estrada1 and S A Fulling2
Show affiliationsFollowing Dirac, Schwartz, and others, distributions are well understood (and widely used in physics) as 'generalized functions'. However, a function with a nonintegrable singularity does not define a distribution automatically or unambiguously. We review a variety of ways in which such distributions can be defined, sometimes with inequivalent results, or results containing arbitrary constants. We give special attention to the function cosech2 x and its semiclassical scaling limit, which have recently attracted some attention in statistical mechanics.
26A30 Singular functions, Cantor functions, functions with other special properties
41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
81T70 Quantization in field theory; cohomological methods (See also 58D29)
Issue 13 (5 April 2002)
Received 29 September 2001, in final form 2 January 2002
Published 22 March 2002
A Corrigendum for this article has been published in 2005 J. Phys. A: Math. Gen. 38 7785
Ricardo Estrada and S A Fulling 2002 J. Phys. A: Math. Gen. 35 3079
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