Stefan Bergman

Stefan Bergman (5 May 1895 – 6 June 1977) was a Polish-born American mathematician whose primary work was in complex analysis. He is best known for the kernel function he discovered while at Berlin University in 1922. This function is known today as the Bergman kernel. Bergman taught for many years at Stanford University, and served as an advisor to several students.^[1]

Biography

Born in Częstochowa, Congress Poland, Russian Empire, Bergman received his Ph.D. at Berlin University in 1921 for a dissertation on Fourier analysis. His advisor, Richard von Mises, had a strong influence on him, lasting for the rest of his career.^[2] In 1933, Bergman was forced to leave his post at the Berlin University because he was a Jew. He fled first to Russia, where he stayed until 1939, and then to Paris. In 1939, he emigrated to the United States, where he would remain for the rest of life.^[2] He was elected a Fellow of the American Academy of Arts and Sciences in 1951.^[3] In 1962 he was an invited speaker at the International Congress of Mathematicians in Stockholm (On meromorphic functions of several complex variables). He died in Palo Alto, California, aged 82.

The Bergman Prize

The Stefan Bergman Prize in mathematics was initiated by Bergman's wife in her will, in memory of her husband's work. The American Mathematical Society supports the prize and selects the committee of judges.^[4] The prize is awarded for:^[4]

1. the theory of the kernel function and its applications in real and complex analysis; or
2. function-theoretic methods in the theory of partial differential equations of elliptic type with a special attention to Bergman's and related operator methods.

Selected publications

• Bergmann, Stefan (1933), "Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande. I", Journal für die reine und angewandte Mathematik (in German) 169: 1–42, doi:10.1515/crll.1933.169.1, JFM 60.1025.01 .
• Bergmann, Stefan (1934), "Über eine in gewissen Bereichen mit Maximumfläche gültige Integraldarstellung der Funktionen zweier komplexer Variabler: I", Mathematische Zeitschrift (in German) 39: 76–94, doi:10.1007/BF01201345, Zbl 0009.26202 .
• Bergmann, Stefan (1935), "Über die Kernfunktion eines Bereiches und ihr Verhalten am Rande. II", Journal für die reine und angewandte Mathematik (in German) 172: 89–128, doi:10.1515/crll.1935.172.89, JFM 60.1025.01 .
• Bergmann, S. (1935), "Über eine in gewissen Bereichen mit Maximumfläche gültige Integraldarstellung der Funktionen zweier komplexer Variabler: II", Mathematische Zeitschrift (in German) 39: 605–608, doi:10.1007/BF01201376, Zbl 61.0372.01 
• Bergmann, S. (1936), "Über eine Integraldarstellung von Funktionen zweier komplexer Veränderlichen", Recueil Mathématique (Matematicheskii Sbornik) N.S. (in German), 1 (43) (6): 851–862, Zbl 0016.17001 
• Bergmann, Stefan (1947) [1941], Sur les fonctions orthogonales de plusieurs variables complexes avec les applications à la théorie des fonctions analytiques., Mémorial des sciences mathématiques (in French) 106 (2nd ed.), Paris: Gauthier-Villars, p. 61, JFM 67.0299.03, MR 32776, Zbl 0036.05101 . The original edition was published in 1941 by Interscience Publishers.^[5]
• Bergmann, Stefan (1948), Sur la fonction-noyau d'un domaine et ses applications dans la théorie des transformations pseudo-conformes., Mémorial des sciences mathématiques (in French) 108, Paris: Gauthier-Villars, p. 80, MR 32777, Zbl 0036.05201 .^[6]
• The Kernel Function and Conformal Mapping, American Mathematical Society 1950,^[7] 2nd edn. 1970
• with Menahem Max Schiffer: Kernel Functions and elliptic differential equations in mathematical physics, Academic Press 1953^[8]
• with Heriot: Application of the method of the kernel function for solving boundary value problems, Numerische Mathematik 3, 1961
• Integral operators in the theory of linear partial differential equations, Springer 1961,^[9] 2nd edn. 1969

See also

• Bergman kernel
• Bergman space
• Bergman–Weil integral representation

References