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A partition of unity is a mathematical concept in geometry. I want to know when and in what context this concept appeared.

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Partitions of unity were formally introduced by Dieudonne (C. R. 205 (1937) 593-595), and for some time they were even called "Dieudonne decompositions". However is some special cases they were used by Whitney (TAMS, 36 (1934) 63-89). This information is taken from Hormander, Analysis of Partial differential operators, vol. I, comments to Chapter I.

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  • $\begingroup$ I don't know if it is the same concept that Dieudonne used, but the term "Zerlegung der Einheit" appeared already in John von Neumann's 1929 paper on Hermitian operators in a Hilbert space: gdz.sub.uni-goettingen.de/dms/load/img/… $\endgroup$
    – Jan Peter Schäfermeyer
    May 10, 2017 at 19:40
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    $\begingroup$ I suppose this is a different partition of different "unity" which von Neuman used: a representation of the unity operator as a sum of projectors. Dieudonne (and I) meant a representation of the functon "one" as a sum of functions with compact support. $\endgroup$
    – Alexandre Eremenko
    May 10, 2017 at 20:14
  • $\begingroup$ Yes, what von Neumann did is today called resolution of the identity $\endgroup$
    – Jan Peter Schäfermeyer
    Jul 28, 2017 at 22:25

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