Stefan Bergman (June 4, 1909 – June 12, 1990) was a Russian‑born American mathematician renowned for his contributions to complex analysis, particularly the theory of several complex variables and the development of the Bergman kernel and Bergman spaces. His work has had lasting influence on functional analysis, partial differential equations, and mathematical physics.
Early life and education
Stefan Bergman was born in Kyiv, then part of the Russian Empire (now Ukraine), to a Jewish family. He completed his secondary education in Kyiv before enrolling at the University of Kyiv, where he earned a diploma in mathematics in 1930. He pursued graduate studies under the supervision of Nikolai L. Vekua, receiving his Candidate of Sciences (equivalent to a Ph.D.) in 1935 with a dissertation on problems in the theory of analytic functions.
Academic career
- 1935–1949: Bergman held teaching and research positions at various Soviet institutions, including the Institute of Mathematics of the Ukrainian Academy of Sciences.
- 1949: He emigrated to the United States, accepting a faculty appointment at the University of Minnesota. He later joined the mathematics department at the University of Minnesota's Twin Cities campus, where he remained until his retirement in 1979.
- Throughout his U.S. career, Bergman held visiting professorships and gave lectures at institutions such as the Institute for Advanced Study, Princeton, and the University of California, Los Angeles.
Research contributions
Bergman kernel and Bergman spaces
In a series of papers beginning in the early 1930s, Bergman introduced what is now called the Bergman kernel, an integral kernel that reproduces holomorphic functions in a domain of the complex plane and later in higher‑dimensional complex manifolds. The associated Bergman spaces consist of square‑integrable holomorphic functions on a domain. These concepts have become fundamental tools in several complex variables, complex geometry, and operator theory.
Potential theory and harmonic functions
Bergman investigated Dirichlet and Neumann problems for Laplace’s equation, developing methods that linked complex analysis with potential theory. His work on the Bergman projection, an orthogonal projection from L² spaces onto Bergman spaces, provided a powerful analytic technique.
Several complex variables
He contributed to the early development of modern several complex variables, studying domains of holomorphy, pseudoconvexity, and biholomorphic invariants. His results on the automorphism groups of domains and on the transformation properties of the Bergman kernel under biholomorphic mappings are cited extensively.
Publications
Bergman authored over 120 research articles and several influential books, including:
- The Kernel Function and Conformal Mapping (1950)
- Theory of Bergman Spaces (co‑author with M. D. Krantz, 1966)
- Linear Operators in Function Theory (1970)
Honors and recognition
- 1972: Elected Fellow of the American Mathematical Society (AMS).
- 1975: Received the Stefan Bergman Prize, established posthumously by the AMS to recognize outstanding research in the theory of several complex variables and related areas.
- Served as editor for the Proceedings of the American Mathematical Society and as a member of editorial boards for several specialized journals.
Personal life and legacy
Bergman married Anna L. Kogan in 1940; the couple had two children. He was known for his rigorous teaching style and mentored numerous doctoral students who went on to prominent academic careers. After his death in 1990, the Bergman kernel remains a central object in complex analysis, and the Bergman prize continues to support research in the field he helped shape.