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Nov 3, 2019 at 14:04 comment added Tom Copeland See, e.g., the OP's paper "A Cauchy–Dirac delta function" by Mikhail G. Katz and David Tall arxiv.org/abs/1206.0119 See Zemanian "Distribution theory and transform analysis" for precise discussions of different nascent delta functions.
Apr 15, 2013 at 23:49 comment added Tom Copeland Really, weren't the results for the limiting case of the derivative of the log worked out fairly rigorously by Cauchy and Poisson in their work on potential theory long before 20'th century mathematicians put a formal dress on them?
Apr 15, 2013 at 18:42 history edited jbc CC BY-SA 3.0
small addition on why the logarithm of the absolute value is a distribution
Apr 15, 2013 at 18:36 history answered jbc CC BY-SA 3.0