Herz–Schur multiplier

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 ²(G)) with respect to the weak topology, λ is the left regular representation of G and Ψ is on M defined as

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \Psi:~\sum\limits_{g\in G}\mu_g\lambda_g\mapsto\sum\limits_{g\in G}\psi(g)\mu_g\lambda_g.

See also

• Figà-Talamanca–Herz algebra
• Fourier algebra

References

• 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.