Person: Bergman, Stefan
Stefan Bergman was a Polish-born American mathematician whose primary work was in complex analysis.
Mathematical Profile (Excerpt):
- Stefan's parents were Bronislaw Bergman and Tekla Herc.
- Stefan was brought up in Czestochowa where he attended primary school and then the gymnazie (the local Gymnasium).
- Von Mises strongly influenced Bergman and this influence had a continuing impact on his scientific work for the rest of his career.
- Bergman worked for his doctorate under von Mises' supervision, and was awarded the degree in 1922 for his thesis Über die Entwicklung der harmonischen Funktionen der Ebene und des Raumes nach Orthogonalfunktionen Ⓣ(On the development of harmonic functions of the plane and of space by orthogonal functions).
- Its results were applied, on the one hand, to fluid dynamics, conformal mapping and potential theory and led, on the other hand, to the "Bergman kernel function" which is one of his major achievements in pure mathematics.
- Perhaps it was Bergman's deep understanding of both pure and applied mathematics which let him develop powerful method in potential theory which he applied to electrical engineering, elasticity and fluid flow.
- In 1930 Bergman was appointed as a privatdozent in both the Institute for Mathematics and the Institute for Applied Mathematics at the University of Berlin with an habilitation thesis on the behaviour of kernel functions on the boundary of their domains.
- It was highly unusual for anyone to obtain a post in both Institutes, but entirely appropriate in Bergman's case.
- Bergman was forced to flee for the third time, going to the United States with von Mises as his sponsor.
- Several years ago Stefan Bergman discovered that essentially the same is true for a vast class of partial differential equations which includes the potential equation as the simplest case.
- Bergman gave explicit formulae which allow a solution of a given differential equation to derive from an arbitrarily chosen analytic function (in some instances from a pair of real functions) and proved that all solutions can be derived in this way.
- Now, two of Bergman's pupils, Bers and Gelbart, found that in a special case the analogy can be carried much farther.
- Though all solutions obtained by Bers and Gelbart can be derived by Bergman's methods also, it must be expected that the new approach will prove very useful.
- Bergman is best known for his research in several complex variables, as well as the Bergman projection and, as was mentioned above, the Bergman kernel function which he invented in 1922 while at Berlin University.
- In 1953 Bergman and Schiffer published Kernel functions and elliptic differential equations in mathematical physics.
- Bergman published Integral operators in the theory of linear partial differential equations in 1961.
- In 1974 Charles Fefferman found a deep application of Bergman's ideas to biholomorphic mappings and a conference on several complex variables, held in 1975, had Bergman's work as its main theme.
- Bergman attended the conference, clearly enjoying the central role of his work.
- Awards are made every year or two in: 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 attention to Bergman's operator method.
Born 5 May 1895, Częstochowa, Russian Empire (now Poland). Died 6 June 1977, Palo Alto, California, USA.
View full biography at MacTutor
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Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive