Resumen de The wavelet transforms in Gelfand–Shilov spaces

Stevan Pilipovic, Dušan Rakić, Nenad Teofanov, Jasson Vindas

• We describe local and global behavior of wavelet transforms of ultra-differentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand–Shilov type spaces and their dual spaces. In particular, we introduce a new family of highly time-scale localized spaces on the upper half-space. We study the wavelet synthesis operator (the left-inverse of the wavelet transform) and obtain the resolution of identity (Calderón reproducing formula) in the context of ultradistributions.