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Fractional-Wavelet Analysis of Positive definite Distributions and Wavelets on D’(C)
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-3320-1493
Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics. (MAM)ORCID iD: 0000-0003-4554-6528
2016 (English)In: Engineering Mathematics II: Algebraic, Stochastic and Analysis Structures for Networks, Data Classification and Optimization / [ed] Silvestrov, Sergei; Rančić, Milica, Springer, 2016, 337-353 p.Chapter in book (Refereed)
Abstract [en]

In the following chapter we describe a wavelet expansion theory for positivedefinite distributions over the real line and define a fractional derivative operator for complex functions in the distribution sense. In order to obtain a characterisation of the complex fractional derivative through the distribution theory, the Ortigueira-Caputo fractional derivative operator is rewritten as a convolution product according to the fractional calculus of real distributions. In particular, the fractional derivative of the Gabor-Morlet wavelet is computed together with its plots and main properties.

Place, publisher, year, edition, pages
Springer, 2016. 337-353 p.
Series
Springer Proceedings in Mathematics & Statistics, ISSN 2194-1009 ; 179
Keyword [en]
Wavelet basis, positive definite distribution, complex fractional derivative, Gabor-Morlet wavelet.
National Category
Computational Mathematics Mathematical Analysis
Research subject
Mathematics/Applied Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-33256DOI: 10.1007/978-3-319-42105-6_16Scopus ID: 2-s2.0-85012884806ISBN: 978-3-319-42104-9 (print)ISBN: 978-3-319-42105-6 (print)OAI: oai:DiVA.org:mdh-33256DiVA: diva2:974556
Available from: 2016-09-26 Created: 2016-09-26 Last updated: 2017-03-02Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • ieee
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  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
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  • asciidoc
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