Analytic signals and harmonic measures. (English) Zbl 1082.94006

Qian, Tao

J. Math. Anal. Appl. 314, No. 2, 526-536 (2006).

The author proves that the NASC for \(He^{i \Theta (s)} = - ie^{i \Theta (s)}\), where \(H\) is the Hilbert transformation, \(\Theta\) is a continuous and strictly increasing function with \(| \Theta (\mathbb R)| = 2 \pi\), is such that \(d \Theta (s)\) is a harmonic measure on the line.
The author also proves the periodic case. Further, the author introduces the theory of Hardy-space-preserving weighted trigonometric series and Fourier transformations induced by harmonic measures.

Reviewer: Arjun K. Gupta (Bowling Green)

MSC:

94A12	Signal theory (characterization, reconstruction, filtering, etc.)
42B35	Function spaces arising in harmonic analysis

Keywords:

harmonic measure; Möbius transformation; trigonometric system; Hilbert transformation; time-frequency analysis

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