ABSTRACT
In his 1912 famous paper on integral equations, David Hilbert (1862−1943) introduced an integral transformation, which is now known as the Hilbert transform. Although it was named after Hilbert, the Hilbert transform and its basic properties were developed mainly by G.H. Hardy (1924) and simultaneously by E.C. Titchmarsh during 1925−1930. On the other hand, T.J. Stieltjes (1856−1894) introduced the Stieltjes transform in his studies on continued fractions. This transform was also involved in Stieltjes’ moment problems.
