Erik Holmgren
Erik Albert Holmgren (* July 7, 1872 , † March 18, 1943 ) was a Swedish mathematician who dealt with partial differential equations .
Holmgren was the son of mathematician Hjalmar Holmgren (1822-1885), professor at the Stockholm University of Technology. Holmgren received his PhD in differential equations from Uppsala University in 1898 . He was a professor in Uppsala from 1909 to 1937. In 1924 he became a member of the Academy of Sciences in Uppsala.
He is known for Holmgren's theorem of uniqueness for linear partial differential equations with real analytic coefficients. It says that a solution to the Cauchy problem (with Cauchy data on a non-characteristic surface S) in the vicinity of S has a unique solution. The theorem thus intensifies the (more generally valid) theorem of Cauchy-Kowalewskaja in the linear case, which ensures the existence of an analytical solution and leaves the existence of non-analytical solutions open. According to Holmgren's theorem, there are no further solutions in the linear case.
Torsten Carleman is one of his doctoral students .
Individual evidence
- ^ Mathematics Genealogy Project
- ↑ Holmgren On systems of linear partial differential equations , Öfversigt af Kongl. Vetenskaps-Academien Förhandlinger, 58 (1901), 91-103
| personal data | |
|---|---|
| SURNAME | Holmgren, Erik |
| ALTERNATIVE NAMES | Holmgren, Erik Albert (full name) |
| BRIEF DESCRIPTION | Swedish mathematician |
| DATE OF BIRTH | July 7, 1872 |
| DATE OF DEATH | March 18, 1943 |