Generalized Krein algebras and asymptotics of Toeplitz determinants
| dc.creator | Böttcher, Albrecht | |
| dc.creator | Karlovich, Alexei | |
| dc.creator | Silbermann, Bernd | |
| dc.date | 2006-12-18 | |
| dc.date.accessioned | 2026-07-07T07:35:41Z | |
| dc.date.available | 2026-07-07T07:35:41Z | |
| dc.description | We give a survey on generalized Krein algebras $K_{p,q}^{α,β}$ and their applications to Toeplitz determinants. Our methods originated in a paper by Mark Krein of 1966, where he showed that $K_{2,2}^{1/2,1/2}$ is a Banach algebra. Subsequently, Widom proved the strong Szegő limit theorem for block Toeplitz determinants with symbols in $(K_{2,2}^{1/2,1/2})_{N\times N}$ and later two of the authors studied symbols in the generalized Krein algebras $(K_{p,q}^{α,β})_{N\times N}$, where $λ:=1/p+1/q=α+β$ and $λ=1$. We here extend these results to $0<λ<1$. The entire paper is based on fundamental work by Mark Krein, ranging from operator ideals through Toeplitz operators up to Wiener-Hopf factorization. | |
| dc.description | 27 pages | |
| dc.identifier | https://arxiv.org/abs/math/0612487 | |
| dc.identifier | http://arxiv.org/abs/math/0612487 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/120174 | |
| dc.subject | Functional Analysis | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 47B35; 15A15; 47B10 | |
| dc.title | Generalized Krein algebras and asymptotics of Toeplitz determinants | |
| dc.type | text |