Аннотация:
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.
Ключевые слова и фразы: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.
Полный текст:
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