Mathematical analysts

Joseph Leo Doob (February 27, 1910 – June 7, 2004) was an American mathematician, specializing in analysis and probability theory.
The theory of martingales was developed by Doob.

Halsey Lawrence Royden, Jr. (September 26, 1928 – August 22, 1993) was an American mathematician, specializing in complex analysis on Riemann surfaces, several complex variables, and complex differential geometry. Royden is the author of a popular textbook on real analysis.

Louis de Branges de Bourcia (born August 21, 1932) is a French-American mathematician. He was the Edward C. Elliott Distinguished Professor of Mathematics at Purdue University in West Lafayette, Indiana, retiring in 2023. He is best known for proving the long-standing Bieberbach conjecture in 1984, now called de Branges's theorem. He claims to have proved several important conjectures in mathematics, including the generalized Riemann hypothesis.
Born to American parents who lived in Paris, de Branges moved to the US in 1941 with his mother and sisters. His native language is French. He did his undergraduate studies at the Massachusetts Institute of Technology (1949–53), and received a PhD in mathematics from Cornell University (1953–57). His advisors were Wolfgang Fuchs and then-future Purdue colleague Harry Pollard. He spent two years (1959–60) at the Institute for Advanced Study and another two (1961–62) at the Courant Institute of Mathematical Sciences. He was appointed to Purdue in 1962.
An analyst, de Branges has made incursions into real, functional, complex, harmonic (Fourier) and Diophantine analyses. As far as particular techniques and approaches are concerned, he is an expert in spectral and operator theories.

Alice Jeanne LaDuke (born June 27, 1938) is an American mathematician who specialized in mathematical analysis and the history of mathematics. She was also a child actress who appeared in one film (The Green Promise).

Pierre Lelong (14 March 1912 Paris – 12 October 2011) was a French mathematician who introduced the Poincaré–Lelong equation, the Lelong number and the concept of plurisubharmonic functions.

Konrad Hermann Theodor Knopp (22 July 1882 – 20 April 1957) was a German mathematician who worked on generalized limits and complex functions.

Giuseppe Vitali (26 August 1875 – 29 February 1932) was an Italian mathematician who worked in several branches of mathematical analysis. He gives his name to several entities in mathematics, most notably the Vitali set with which he was the first to give an example of a non-measurable subset of real numbers.

Giovanni Sansone (24 May 1888 – 13 October 1979) was an Italian mathematician, known for his works on mathematical analysis, on the theory of orthogonal functions and on the theory of ordinary differential equations.He was an Invited Speaker of the ICM in Bologna in 1928.

Paul Matthieu Hermann Laurent (2 September 1841 in Luxembourg City – 19 February 1908 in Paris, France) was a French mathematician. Despite his large body of works, Laurent series expansions for complex functions were not named after him, but after Pierre Alphonse Laurent.

Guido Fubini (19 January 1879 – 6 June 1943) was an Italian mathematician, known for Fubini's theorem and the Fubini–Study metric.