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The wavelet transforms in Gelfand-Shilov spaces

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.

preprint2015arXivOpen access
Stevan PilipovicDusan RakicNenad TeofanovJasson Vindas
math.FA
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Stevan PilipovicDusan RakicNenad TeofanovJasson Vindas

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