nLab Bochner's theorem

This entry is about Bochner’s theorem in harmonic analysis. For the Bochner linearization theorem in (on transformation groups) see there.

Statement

(…)

Related concepts

• Fourier transform

• harmonic analysis

• kernel method

References

For abelian groups

Named after Salomon Bochner.

Textbook accounts:

• Edwin Hewett, Kenneth Ross, Section 33 of: Abstract Harmonic Analysis, Volume II: Structure and Analysis for Compact Groups, Analysis on Locally Compact Abelian Groups, Grundlehren der mathematischen Wissenschaften 152, Springer 1970 (doi:10.1007/978-3-662-26755-4)

See also

• Wikipedia, Bochner’s theorem

For non-abelian groups

Generalization to non-abelian groups:

• Hewett-Ross 70, Section 34

Discussion in the context of kernel methods:

• Kenji Fukumizu, Bharath Sriperumbudur, Arthur Gretton, Bernhard Schölkopf, Characteristic Kernels on Groups and Semigroups, Advances in Neural Information Processing Systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008 (NIPS 2008), 473-480 (mpg:5466, pdf)