Asymptotics for Some Non-classical Conormal Distributions Whose Symbols Contain Negative Powers of

摘要

We examine distributions on whose Fourier coefficients are of the form , and variants. These distributions are smooth except at , and the nature of their singularities at turns out to be much more complex than those of their counterparts that involve positive powers of . We also study related Fourier transforms. We move from one dimension to higher dimensions, where a wider variety of phenomena arise, and more subtle analytical techniques are called for.