Hilbert transform of

Author:
Javad Mashreghi

Journal:
Proc. Amer. Math. Soc. **130** (2002), 683-688

MSC (2000):
Primary 30D20; Secondary 42A50

DOI:
https://doi.org/10.1090/S0002-9939-01-06335-3

Published electronically:
July 31, 2001

MathSciNet review:
1866020

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Abstract | References | Similar Articles | Additional Information

There are two general ways to evaluate the Hilbert transform of a function of real variable . We can extend to a harmonic function in the upper half plane by the Poisson integral formula. Non-tangential limit of its harmonic conjugate exists almost everywhere and is defined to be the Hilbert transform of . There is also a singular integral formula for the Hilbert transform of . It is fairly difficult to directly evaluate the Hilbert transform of . In this paper we give an explicit formula for the Hilbert transform of , where is a function in the Cartwright class.

**1.**Paul Koosis,*The Logarithmic Integral I*, Cambridge Studies in Advanced Mathematics 12, 1988. MR**90a:30097****2.**John B. Conway,*Functions of one complex variable*, Second Edition, Springer-Verlag, 1978. MR**80c:30003****3.**A. Zygmund,*Trigonometric Series*, Cambridge, 1968. MR**58:29731****4.**R. Boas,*Entire Functions*, Academic Press, 1954. MR**16:914f**

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Additional Information

**Javad Mashreghi**

Affiliation:
Department of Mathematics and Statistics, McGill University, Montreal, Canada H3A 2K6

Email:
mashregh@math.mcgill.ca

DOI:
https://doi.org/10.1090/S0002-9939-01-06335-3

Keywords:
Entire functions of exponential type,
Blaschke products,
Hilbert transform

Received by editor(s):
August 2, 2000

Published electronically:
July 31, 2001

Additional Notes:
This work was supported by Institut des sciences mathématiques (Montreal) and a J. W. McConnell McGill Major Fellowship.

Communicated by:
Juha Heinonen

Article copyright:
© Copyright 2001
American Mathematical Society