Bochner's theorem
Theorem of Fourier transforms of Borel measures / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Bochner's theorem?
Summarize this article for a 10 year old
SHOW ALL QUESTIONS
In mathematics, Bochner's theorem (named for Salomon Bochner) characterizes the Fourier transform of a positive finite Borel measure on the real line. More generally in harmonic analysis, Bochner's theorem asserts that under Fourier transform a continuous positive-definite function on a locally compact abelian group corresponds to a finite positive measure on the Pontryagin dual group. The case of sequences was first established by Gustav Herglotz (see also the related Herglotz representation theorem.)[1]
This article is about Bochner's theorem in harmonic analysis. For Bochner's theorem in Riemannian geometry, see Bochner's theorem (Riemannian geometry).