Hankel and Toeplitz operators: continuous and discrete representations - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Opuscula Mathematica Année : 2017

Hankel and Toeplitz operators: continuous and discrete representations

Résumé

We find a relation guaranteeing that Hankel operators realized in the space of sequences $\ell^2 ({\Bbb Z}_{+}) $ and in the space of functions $L^2 ({\Bbb R}_{+}) $ are unitarily equivalent. This allows us to obtain exhaustive spectral results for two classes of unbounded Hankel operators in the space $\ell^2 ({\Bbb Z}_{+}) $ generalizing in different directions the classical Hilbert matrix. We also discuss a link between representations of Toeplitz operators in the spaces $\ell^2 ({\Bbb Z}_{+}) $ and $L^2 ({\Bbb R}_{+}) $.

Dates et versions

hal-01355739 , version 1 (24-08-2016)

Identifiants

Citer

Dimitri R Yafaev. Hankel and Toeplitz operators: continuous and discrete representations. Opuscula Mathematica, 2017, ⟨10.74994/OpMath.2017.37.1.189⟩. ⟨hal-01355739⟩
169 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More