Result: Properties of ultradistributions having the S-asymptotics: Properties of ultradistributions having the \(S\)-asymptotics
Further Information
The \(S\)-asymptotics was originally defined by L. Schwartz in his famous books on distribution theory. This notion was deeply elaborated by the authors in a series of papers, with numerous applications to the theory of PDEs. In the paper under review, the authors extend the \(S\)-asymptotics to the spaces of ultradistributions, both of Beurling and Roumieu type [see \textit{H. Komatsu}'s paper ``Ultradistributions. I: Structure theorems and a characterization'', J. Fac. Sci., Tokyo Univ., Sect. I A 20, 25-105 (1973; Zbl 0258.46039)]. They find sufficient and necessary conditions for the existence of \(S\)-asymptotics and compare it to the same notion in the space of distributions. Also, the \(S\)-asymptotics of the solution \(U\) of the equation \(P(D)U = F,\) for an ultradifferential operator \(P(D)\), is analyzed.