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arXiv · 1405.0111

The wavelet transforms in Gelfand-Shilov spaces

Stevan Pilipovic·Dusan Rakic·Nenad Teofanov·Jasson Vindas
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Abstract

We describe local and global properties of wavelet transforms of ultradifferentiable functions. The results are given in the form of continuity properties of the wavelet transform on Gelfand-Shilov type spaces and their duals. 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.

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Stevan Pilipovic, Dusan Rakic, Nenad Teofanov, Jasson Vindas. 2015-08-24. The wavelet transforms in Gelfand-Shilov spaces. https://doi.org/10.1007/s13348-015-0154-y

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