Characterization of boundary values of functions in Hardy spaces with applications in signal analysis. (English) Zbl 1086.30035

Qian, Tao

J. Integral Equations Appl. 17, No. 2, 159-198 (2005).

Let \(H(f)(t)\) be the Hilbert transform of a function \(f\) defined on the real line. The author characterizes triples of functions \((\rho,c,s)\) satisfying the equation \[ H(\rho (\cdot)c(\cdot))(t)=\rho (t)s(t), c^2+s^2=1, \rho (t)\geq 0. \]

Reviewer: Alexander I. Kheyfits (Bronx)

MSC:

30D55

\(H^p\)-classes (MSC2000)

Keywords:

Hardy spaces; boundary values; Hilbert transform

References:

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