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Eurasian Mathematical Journal, 2014, Volume 5, Number 1, Pages 95–121 (Mi emj151)  
This article is cited in 6 scientific papers (total in 6 papers)

The real and complex techniques in harmonic analysis from the point of view of covariant transform

V. V. Kisil

School of Mathematics, University of Leeds, Leeds LS29JT, UK
Full-text PDF (537 kB) Citations (6)
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Abstract: This paper reviews complex and real techniques in harmonic analysis. We describe the common source of both approaches rooted in the covariant transform generated by the affine group.
Keywords and phrases: wavelet, coherent state, covariant transform, reconstruction formula, the affine group, $ax+b$-group, square integrable representations, admissible vectors, Hardy space, fiducial operator, approximation of the identity, atom, nucleus, atomic decomposition, Cauchy integral, Poisson integral, Hardy–Littlewood maximal function, grand maximal function, vertical maximal function, non-tangential maximal function, intertwining operator, Cauchy–Riemann operator, Laplace operator, singular integral operator (SIO), Hilbert transform, boundary behaviour, Carleson measure, Littlewood–Paley theory.
Received: 12.09.2013
Document Type: Article
MSC: Primary 42-02; Secondary 42A20, 42B20, 42B25, 42B35, 42C40, 43A50, 43A80
Language: English
Citation: V. V. Kisil, “The real and complex techniques in harmonic analysis from the point of view of covariant transform”, Eurasian Math. J., 5:1 (2014), 95–121
Citation in format AMSBIB
\Bibitem{Kis14}
\by V.~V.~Kisil
\paper The real and complex techniques in harmonic analysis from the point of view of covariant transform
\jour Eurasian Math. J.
\yr 2014
\vol 5
\issue 1
\pages 95--121
\mathnet{http://mi.mathnet.ru/emj151}
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    • This publication is cited in the following 6 articles:
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