Hilbert Transform in the Cartwright–de Branges Space
摘要
Contrary to celebrated transforms such as the Fourier transform, explicit formulas for the Hilbert transform of well-known functions are rare. In this note, we present a formula for the Hilbert transform of \(\log |F/E|\) , where F belongs to the Cartwright–de Branges space associated with the de Branges function E. The formula implies several other known results.