Hilbert Transform, Nevanlinna Class and Toeplitz Kernels

In this article we obtain an explicit formula for the Hilbert transform of \(\log |f|,\) $log|f|,$ for the function f in Nevanlinna class having continuous extension to the real line. This family is the largest possible for which such a formula for the Hilbert transform of \(\log |f|,\) $log|f|,$ can be obtained. The formula is very general and implies several previously known results.