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Fractional-wavelet analysis of positive definite distributions and wavelets on \({\mathcal D'(\mathbb {C})}\). (English) Zbl 1365.65294
Silvestrov, Sergei (ed.) et al., Engineering mathematics. II: Algebraic, stochastic and analysis structures for networks, data classification and optimization. Cham: Springer (ISBN 978-3-319-42104-9/hbk; 978-3-319-42105-6/ebook). Springer Proceedings in Mathematics & Statistics 179, 337-353 (2016).
The Ortigueira-Caputo fractional operator, which provides the fractional derivative of a complex function, is rewritten in the distribution sense. The fractional derivative of the Gabor-Morlet wavelet is computed. An open problem, concerning the possibility to generalize the reconstruction formula for Shannon wavelets through the distribution theory, is proposed.
For the entire collection see [Zbl 1365.74007].

MSC:
65T60 Numerical methods for wavelets
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