Regularly varying generalized functions

Abstract

Karamata's definition of regularly varying functions (see Kararnata⁴) is cstended to generalized functions which have been defined as elements of a dual space of a basic vector topological space. Some special properties of regularly varying Fourier hyperfunctions are proved and the obtained results are appli~d to equations with local operators.

Keywords:

• regular variation
• generalized function
• fourier hyperfunctions