Title

How singular functions define distributions

Document Type

Article

Publication Date

4-5-2002

Abstract

Following 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 cosech 2 x and its semiclassical scaling limit, which have recently attracted some attention in statistical mechanics.

Publication Source (Journal or Book title)

Journal of Physics A: Mathematical and General

First Page

3079

Last Page

3089

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