@Article{Yafaev2017,
author = "Yafaev, Dmitri R.",
title = "Hankel and Toeplitz operators: continuous and discrete representations",
journal = "Opuscula Math.",
year = "2017",
volume = "37",
number = "1",
pages = "189--218",
doi = "http://dx.doi.org/10.7494/OpMath.2017.37.1.189",
url = "http://dx.doi.org/10.7494/OpMath.2017.37.1.189",
abstract = "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 \(L^2 (\mathbb{R}_{+})\).",
keywords = "unbounded Hankel and Toeplitz operators, various representations, moment problems, generalized Hilbert matrices",
issn = "1232-9274"
}