Representation of quasianalytic ultradistributions (Q1312336)

The authors deal with a representation theorem for a class of quasianalytic ultradistributions; they show that every ultradistribution in this class can be written as \(u= P(\Delta) g(x)+ h(x)\), where \(g(x)\) is a bounded continuous function, \(h(x)\) is a bounded real analytic function and \(P(d/dt)\) is an ultradifferential operator. It is shown also that the boundary value of every heat function with some exponential growth condition determines an ultradistribution in this class. We mention that this theorem does not exclude non-quasianalytic classes.