Truncation and Duality Results for Hopf Image Algebras

• Autorzy: Teodor Banica
• Języki publikacji: EN

Abstrakty

EN

Associated to an Hadamard matrix $H ∈ M_N(ℂ)$ is the spectral measure μ ∈ 𝓟[0,N] of the corresponding Hopf image algebra, A = C(G) with $G ⊂ S⁺_N$. We study a certain family of discrete measures $μ^r ∈ 𝓟[0,N]$, coming from the idempotent state theory of G, which converge in Cesàro limit to μ. Our main result is a duality formula of type $∫_0^N (x/N)^p dμ^r(x) = ∫_0^N (x/N)^r dν^p(x)$, where $μ^r,ν^r$ are the truncations of the spectral measures μ,ν associated to $H,H^t$. We also prove, using these truncations $μ^r,ν^r$, that for any deformed Fourier matrix $H=F_M ⊗_Q F_N$ we have μ = ν.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2014
• Tom: 62
• Numer: 2
• Strony: 161-179

Daty

wydano

2014

Twórcy

autor

Teodor Banica

• Department of Mathematics, Cergy-Pontoise University, 95000 Cergy-Pontoise, France

Identyfikatory

DOI

10.4064/ba62-2-5