TY  - JOUR
ID  - Yafaev2017
LB  - Yafaev2017
AU  - Yafaev, Dmitri R.
TI  - Hankel and Toeplitz operators: continuous and discrete representations
ST  - Hankel and Toeplitz operators: continuous and discrete representations
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2017
VL  - 37
IS  - 1
SP  - 189
EP  - 218
DO  - http://dx.doi.org/10.7494/OpMath.2017.37.1.189
UR  - http://dx.doi.org/10.7494/OpMath.2017.37.1.189
AB  - We find a relation guaranteeing that Hankel operators realized in the space of sequences \(\mathcal{l}^2 (\mathbb{Z}_{+})\) and in the space of functions \(L^2 (\mathbb{R}_{+})\) are unitarily equivalent. This allows us to obtain exhaustive spectral results for two classes of unbounded Hankel operators in the space \(\mathcal{l}^2 (\mathbb{Z}_{+})\) generalizing in different directions the classical Hilbert matrix. We also discuss a link between representations of Toeplitz operators in the spaces \(\mathcal{l}^2 (\mathbb{Z}_{+})\) and \(L^2 (\mathbb{R}_{+})\).
KW  - unbounded Hankel and Toeplitz operators
KW  - various representations
KW  - moment problems
KW  - generalized Hilbert matrices
SN  - 1232-9274
ER  -