Torsten Carleman
| Torsten Carleman | |
|---|---|
| Born |
8 July 1892 Visseltofta |
| Died | 11 January 1949 (aged 56) Stockholm |
| Nationality | Swedish |
| Fields | Mathematics |
| Institutions |
Lund University Mittag-Leffler Institute |
| Alma mater | Uppsala University |
| Doctoral advisor | Erik Albert Holmgren |
| Doctoral students | Ulf Hellsten Karl Persson (Dagerholm) Åke Pleijel Hans Rådström |
| Known for |
Carleman's condition Carleman's inequality Denjoy–Carleman theorem mean ergodic theorem Carleman kernel Carleman formulae |
Torsten Carleman (8 July 1892, Visseltofta, Osby Municipality – 11 January 1949, ), born Tage Gillis Torsten Carleman, was a Swedish mathematician, known for his results in classical analysis and its applications. As the director of the Mittag-Leffler Institute for more than two decades, Carleman was the most influential mathematician in Sweden.
The dissertation of Carleman under Erik Albert Holmgren, as well as his work in the early 1920s, was devoted to singular integral equations. He developed the spectral theory of integral operators with Carleman kernels, that is, kernels K(x, y) such that K(y, x) = K(x, y) for almost every (x, y), and
for almost every x.
In the mid-1920s, Carleman developed the theory of quasi-analytic functions. He proved the necessary and sufficient condition for quasi-analyticity, now called the Denjoy–Carleman theorem. As a corollary, he obtained a sufficient condition for the determinacy of the moment problem. As one of the steps in the proof of the Denjoy–Carleman theorem in Carleman (1926), he introduced the Carleman inequality
valid for any sequence of non-negative real numbers ak.
At about the same time, he established the Carleman formulae in complex analysis, which reconstruct an analytic function in a domain from its values on a subset of the boundary. He also proved a generalisation of Jensen's formula, now called the Jensen–Carleman formula.
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