The Real and Complex Techniques in Harmonic Analysis from the Point of View of Covariant Transform


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Authors

  • Vladimir V. Kisil

Keywords:

wavelet, coherent state, covariant transform, reconstruction formula, the affine group, square integrable representations, admissible vectors, Hardy space, fiducial operator, approximation of the identity, atom, nucleus, atomic decomposition, \( \text{Cauchy integral} \), \( \text{Poisson integral} \), Hardy--Littlewood maximal function, grand maximal function, vertical maximal function, non-tangential maximal function, intertwining operator, \( \text{Cauchy-Riemann operator} \), \( \text{Laplace operator} \), singular integral operator (SIO), \( \text{Hilbert transform} \), boundary behaviour, Carleson measure, Littlewood--Paley theory

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.

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Published

2014-03-30

How to Cite

Kisil, V. V. (2014). The Real and Complex Techniques in Harmonic Analysis from the Point of View of Covariant Transform. Eurasian Mathematical Journal, 5(1), 95–121. Retrieved from https://emj.enu.kz/index.php/main/article/view/564

Issue

Vol. 5 No. 1 (2014)

Section

Articles