How singular functions define distributions
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
Estrada, R., & Fulling, S. (2002). How singular functions define distributions. Journal of Physics A: Mathematical and General, 35 (13), 3079-3089. https://doi.org/10.1088/0305-4470/35/13/304