Some contributions to analysis: A new space of generalized functions for integro-differential equations involving Hilbert transforms, and a note on the non-nuclearity of a space of test functions on Hilbert space.

摘要

n part one we investigate the equation P(D,H)F = G, where P is a constant coefficient polynomial in the differential operator D and Hilbert transform operator H, and F & G are elements of certain dual spaces. We construct a space of test functions ;In part two we consider the space