Fritz David Carlson (23 July 1888 – 28 November 1952) was a Swedish mathematician.
After the death of Torsten Carleman, he headed the Mittag-Leffler Institute.
Carlson's contributions to analysis include Carlson's theorem, the Polyá–Carlson theorem on rational functions, and Carlson's inequality
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{\displaystyle \left(\sum _{n=1}^{\infty }|a_{n}|\right)^{4}\leq \pi ^{2}\sum _{n=1}^{\infty }|a_{n}|^{2}\,\sum _{n=1}^{\infty }n^{2}|a_{n}|^{2}~.}
In number theory, his results include Carlson's theorem on Dirichlet series.
Hans Rådström, Germund Dahlquist, and Tord Ganelius were among his students.