In the mathematical field of representation theory, a Herz–Schur multiplier (named after Carl S. Herz and Issai Schur) is a special kind of mapping from a group to the field of complex numbers.
Definition
Let Ψ be a mapping of a group G to the complex numbers. It is a Herz–Schur multiplier if the induced map Ψ: N(G) → N(G) is a completely positive map, where N(G) is the closure of the span M of the image of λ in B(ℓ(G)) with respect to the weak topology, λ is the left regular representation of G and Ψ is on M defined as
See also
References
This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Herz–Schur multiplier" – news · newspapers · books · scholar · JSTOR (June 2009) (Learn how and when to remove this message) |
- Pisier, Gilles (1995), "Multipliers and lacunary sets in non-amenable groups", American Journal of Mathematics, 117 (2), The Johns Hopkins University Press: 337–376, arXiv:math/9212207, doi:10.2307/2374918, ISSN 0002-9327, JSTOR 2374918, MR 1323679, S2CID 2958712
- Figà-Talamanca, Alessandro; Picardello, Massimo A. (1983), Harmonic analysis on free groups, Lecture Notes in Pure and Applied Mathematics, vol. 87, New York: Marcel Dekker Inc., ISBN 978-0-8247-7042-6, MR 0710827
- Carl S. Herz. Une généralisation de la notion de transformée de Fourier-Stieltjes. Annales de l'Institut Fourier, tome 24, no 3 (1974), p. 145-157.
This mathematical analysis–related article is a stub. You can help Misplaced Pages by expanding it. |