The wavelet transforms in Gelfand–Shilov spaces

• Autores: Stevan Pilipovic, Dušan Rakić, Nenad Teofanov, Jasson Vindas
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 67, Fasc. 3, 2016, págs. 443-460
• Idioma: inglés
• DOI: 10.1007/s13348-015-0154-y
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.