Analytic signals and harmonic measures. (English) Zbl 1082.94006

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.


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