Are there any interesting, important or powerful mathematical applications to the Theory of Distributions besides those dealing with partial differential equations?
2026-03-30 17:17:23.1774891043
Applications of the theory of distributions outside of PDEs?
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Applications
The good understanding of the nature of the elements of Sobolev spaces with negative norms.
Representation of functionals and elements of duals in a variety of function spaces.
In Complex Analysis of one variable and several variables, distributions allow to represent functions as convolutions of distributions and particular nice functions.
Help in fractional calculus.
In general every measure, derivative of measure and derivatives of good and no so good functions (with some integrability properties) are distributions, and such "function" appear in most areas of Classical and Modern Analysis. (Take a lot at the books of L. Grafakos.)