Kisil, VV (2014) The Real and Complex Techniques in Harmonic Analysis from the Point of View of Covariant Transform. Eurasian Mathematical Journal, 5 (1). pp. 95-121. ISSN 2077-9879
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.
Metadata
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| Keywords: | 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 |
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| Institution: | The University of Leeds |
| Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
| Depositing User: | Symplectic Publications |
| Date Deposited: | 19 Apr 2016 14:20 |
| Last Modified: | 08 May 2016 08:34 |
| Published Version: | http://emj.enu.kz/images/pdf/2014/5-1-4.pdf |
| Status: | Published |
| Publisher: | Eurasian National University, Kazakhstan |
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