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The wavelet transforms in Gelfand–Shilov spaces

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Abstract

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.

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Authors and Affiliations

  1. Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, 21000, Novi Sad, Serbia

    Stevan Pilipović & Nenad Teofanov

  2. Faculty of Technology, University of Novi Sad, Bul. cara Lazara 1, 21000, Novi Sad, Serbia

    Dušan Rakić

  3. Department of Mathematics, Ghent University, Krijgslaan 281, Gebouw S22, 9000, Ghent, Belgium

    Jasson Vindas

Authors
  1. Stevan Pilipović
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  2. Dušan Rakić
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  3. Nenad Teofanov
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  4. Jasson Vindas
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Corresponding author

Correspondence to Nenad Teofanov.

Additional information

S. Pilipović and N. Teofanov are supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia through Project 174024. D. Rakić is supported by the Ministry of Education, Science and Technological Development of the Republic of Serbia through Project III44006 and by PSNTR through Project 114-451-2167. J. Vindas acknowledges support by Ghent University, through the BOF-Grant 01N01014.

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Pilipović, S., Rakić, D., Teofanov, N. et al. The wavelet transforms in Gelfand–Shilov spaces. Collect. Math. 67, 443–460 (2016). https://doi.org/10.1007/s13348-015-0154-y

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  • DOI: https://doi.org/10.1007/s13348-015-0154-y

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