**Torsten Carleman** was a Swedish mathematician who worked in classical analysis and its applications.

- When people left the seminar and on the way to the restaurant "Rullan" they had to cross the Fyris River, Carleman did not just walk over the bridge, instead he walked on his hands on the railing.
- After Mittag-Leffler's death in 1927, Carleman, who was considered to be the top Swedish mathematician of the time, was appointed as the first director of the Mittag-Leffler Institute.
- However, Carleman was not able to realize plans for a Mathematics Institute, in part because of lack of funds and in part because his personality was more suited to mathematical contemplation than to the kind of entrepreneurship needed to get an Institute off the ground.
- It is certain that Carleman felt that he was the equal of the best mathematicians but also that he was not appreciated according to his merit.
- From 1927 Carleman became an editor of Acta Mathematica.
- Carleman had good relations with many mathematicians, visiting and giving lectures at, Zürich, Göttingen, Oxford, Sorbonne, Nancy and Paris.
- Carleman had several Ph.D. students: N Juringius (1932), F Ehrnst (1938), K Persson (1938), Å Pleijel (1940), U Hellsten (1947), and H Radström (1952).
- As it is often the case with mathematicians who deal with differential or integral equations, Carleman carried a keen interest in the relationship between mathematics and applied sciences.
- During the last period of his life Carleman lived alone in two rooms of the Mittag-Leffler Institute.
- During his last years Carleman suffered from bad health.
- Carleman died on 11 January 1949 in Stockholm.
- Carleman published five books and sixty papers in mathematics.
- There are especially two areas of research, going back to this time, which one can consider as principal works of Carleman.
- Carleman was invited to lecture on this subject at the College of France in April-May 1923.
- Carleman is now remembered for remarkable results in integral equations (1923), quasi-analytic functions (1926), harmonic analysis (1944), trigonometric series (1918-23), approximation of functions (1922-27) and Boltzmann's equation (1944).
- Even in the case of one complex variable the Carleman formula depends on the domain DDD and on the set MMM.
- Carleman wrote also a Textbook in differential and integral calculus together with geometrical and mechanical applications, Stockholm 1928 (2nd ed.
- This is called Carleman linearization or Carleman embedding.
- The unique continuation results as Holmgren and Hörmander theorems are based on a certain type of weighted energy estimate which was introduced by Carleman.
- In 1935 Carleman himself lectured at the Mittag-Leffler Institute on a generalization of the Fourier transformation.
- In June 1947 Carleman participated in a CNRS meeting in Nancy and presented his theory there.
- Carleman lectured at the Sorbonne in 1937 on Boltzmann's equation, which appears in the kinetic theory of gas, and published several papers on this subject.

Born 8 July 1892, Visseltofta, Sweden. Died 11 January 1949, Stockholm, Sweden.

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Origin Sweden

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive