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Fritz Carlson

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23 July 1888

Vimmerby, Sweden

28 Nov 1952

Stockholm, Sweden

Fritz David Carlson was born in Vimmerby, where his father, John Vilhelm Carlson, was a house and land holder; his mother was Lovisa Mathilda Carlson. He studied at secondary schools in Vimmerby (1899-1903) and in Linköping (1903-1907) sitting his final high school graduation examination on 4 June 1907. He matriculated as a student at Uppsala University on 5 September 1907. He was awarded his Master of Science degree on 30 May 1911, Licentiate on 14 December 1912, and defended his Ph.D. thesis On a class of Taylor series on 26 May 1914 (undertaken with the supervision of Anders Wiman), and became Doctor of Philosophy on 30 May 1914.

As a Liljewalch scholar he visited the University of Göttingen during the period January to August 1916, the University of Berlin and the Technical University in Berlin-Charlottenburg from September to December 1916, and as a Thunsk scholar he also visited Paris in 1920.

He was vicarious teacher at the State School in Vimmerby (1910-11), then auxiliary actuary of the Fire and Life Insurance Company Svea (2 June - 8 September 1911). On 3 June 1914 he became docent in mathematics at Uppsala University ( docent in the Swedish system means habilitation in other countries). During the period from 1914 to 1915 he was a deputy at the Teacher Studies in Uppsala, partly as professor of mathematics at Uppsala University (7 May - 27 May 1920) and then, from 9 July 1920, he was appointed as professor of descriptive geometry at the Royal Institute of Technology (KTH) in Stockholm, a post which he held until 1927.

On 8 August 1923 he married a dentist Marie Louise Ljungberger (born on 24 June 1894), a daughter of Johan August Pettersen.

Starting in 1923 he worked for several years as a censor at the student examination. This now historic activity started in 1862 when the universities ceased to have entrance examinations and ended in 1968. The replacement was a flying inspection in which teams of university professors went to the gymnasiums as auditors of the oral examinations and censors when the grades were decided.

Frostman has written about the atmosphere of his work as a censor (see
also , p. 213):

In this task he found ample use not only of his experience of pure mathematics but also of his vast knowledge of literature, history, geography and French literature. Many high school teachers, whose teaching he supervised, keep the memory of a demanding censor with a certain stern sense of humour but also a man of superior comprehension and unfailing judgement.

From 1927 he became a professor of higher mathematical analysis at the Stockholm University College. Carlson was a real professor in the Swedish tradition of that time. We can quote here Garding who wrote in 1997 on page 212 of :

Carlson was one of those who with refined methods continued Mittag-Leffler 's effort in the theory of analytic functions. In his daily life he personified the correct professor ...

and also Kjellberg in 1995 on page 92 of :

He was a perfectionist and he could be strict in social intercourse. I think he liked me because I wrote about somewhat old-fashioned things within function theory. In any case he showed me great kindness. Carlson held a very careful oral examination after a student had been awarded a pass in a written examination. It could happen that he started with a candidate in the morning, sent him for lunch, continued for a couple of hours, and then failed him.

He was a member of the Royal Swedish Academy of Sciences from 1927, the Society of Sciences in Uppsala from 1928, the Royal Physiographic Society of Lund from 1940, and one of the editors of Acta Mathematica from 1930. After Carleman's death in 1949 he administrated the Mittag-Leffler 's Institute.

Carlson had only three Ph.D. students: H Radström (1952), T Ganelius (1953) and G Dahlquist (1958).

Carlson died on 28 November 1952 in Stockholm.

His main work focused on the theory of analytic functions. Some of his most well-known contributions are a theorem connected to the Phragmén-Lindelöf principle, a theorem about the zeros of the V-function and several theorems about power series with integer coefficients. Such names as Carlson inequality, Carlson - Levin constants, Carlson theorem in complex analysis, Pólya - Carlson theorem on rational functions and Carlson theorem on Dirichlet series are well-known in mathematics (see , and ).

Carlson's inequality, proved in 1934, states that:

( |an|)4 π2 |an|2 n2|an|2

and its integral version that

( |f(x)|)4 π2 |f(x)|2 x2|f(x)|2

with the best possible constant π2. Carlson himself obviously believed that his inequality was independent of other inequalities e.g. that of Hölder . Therefore it must have been a big surprise for him when Hardy two years later showed that the inequality even follows from the Schwarz inequality. Different proofs, further generalizations together with some historical remarks and applications in interpolation theory and functional analysis are discussed in , and .

Carlson's theorem in complex analysis, says that if f(z) is an analytic function satisfying |f(z)| Cek|z|, where k < π for Re z 0, and if f(z) = 0 for z = 0, 1, 2, ..., then f(z) is identically zero (cf. ).

Carlson, in a series of papers, investigated Dirichlet series and proved in 1922 that if f(z) = ann-z is convergent in Re z 0 and bounded in every Re z > > 0, then, for each > 0,

|an|2n-2 = limT1/2T |f( + it)|2dt.

Carlson wrote a solid Textbook of geometry in two volumes (Gleerup, Lund, 1943, 1947). This resulted from his teaching at KTH, covering first year geometry at the university. He also published a book Geometry of space (Uppsala, 1949).

At a mature age Carlson could remark that (see , p. 212):

... every mathematician ought to do some work with the Riemann -function.

Carlson published over thirty papers in mathematics.

Source:School of Mathematics and Statistics University of St Andrews, Scotland