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DIFFERENTIAL OPERATORS ON SCHWARTZ DISTRIBUTIONS
https://doi.org/10.1142/S0219887812500624Cited by:0 (Source: Crossref)
Abstract
Differential operators on Schwartz distributions usually are defined as the transpose of differential operators on test functions. However, they do not exhaust all differential operators. In a general setting, Schwartz distributions on sections of compact support of a vector bundle Y over a smooth manifold X are considered. They constitute a C∞(X)-module. We follow a generic algebraic notion of differential operators on a module over a commutative ℝ-ring C∞(X). Such a differential operator on Schwartz distributions is proved to be the transpose of a differential operator on sections of Y → X if and only if it is continuous.
