A formula for the logarithmic derivative and its applications. (English) Zbl 1203.30028
Mashreghi, Javad (ed.) et al., Hilbert spaces of analytic functions. Papers based on the workshop, CRM, Montréal, Canada, December 8–12, 2008. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4879-1/pbk). CRM Proceedings and Lecture Notes 51, 197-201 (2010).
Summary: We show how an explicit formula for the imaginary part of the logarithmic derivative of \(f\), where \(f\) is in the Cartwright class of entire funcitons of exponential type, leads to a new integral representation of the Hilbert transfrom of \(\log| f|\) and also to a representation for the first moment of \(| \widehat f|^2\).
For the entire collection see [Zbl 1188.46002].
For the entire collection see [Zbl 1188.46002].
MSC:
| 30D20 | Entire functions of one complex variable (general theory) |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
