## 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.

### MSC:

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

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