Born in
Vimmerby on 23 July 1888, Fritz David Carlson completed his secondary schooling at
Linköping in 1907 and went on to earn his doctorate at
Uppsala University in 1914 with a thesis on a class of
Taylor series whose
coefficients vary analytically with the index. He was appointed professor of descriptive geometry at the Royal Institute of Technology in Stockholm in 1920 and in 1928 took up the chair of higher analysis at the Stockholm College of Advanced Studies. : \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~. ==References==