Wavelet expansions of analytic hyperfunctions

Abstract

A class of analytic hyperfunctions on the real line is characterized in terms of the wavelet expansions of its members. It is shown that any such analytic hyperfunction can be expanded in a series of wavelets generated by a Meyer—type wavelet. The coefficients of the expansions are shown to satisfy certain growth conditions at infinity.

Keywords:

• hyperfunctions
• generalized functions
• analytic wavelets
• Wavelet expansions

MSC(1991):

• 46F12
• 46F15