hankel and toeplitz operators: continuous and discrete representations
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2017
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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 \(L^2 (\mathbb{R}_{+})\).
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yafaev2017opusculahankel
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| Authors | ;Dmitri R. Yafaev |
| Journal | zhonghua yi xue za zhi |
| Year | 2017 |
| DOI |
http://dx.doi.org/10.7494/OpMath.2017.37.1.189
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