Generalized Signum Function
At real values of, it is possible to define a generalized function–version of the signum function, such that everywhere, including at the point (unlike, for which ). This generalized signum allows construction of the algebra of generalized functions, but the price of such generalization is the loss of commutativity. In particular, the generalized signum anticommutes with the delta-function,
in addition, cannot be evaluated at ; and the special name, is necessary to distinguish it from the function . ( is not defined, but .)
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