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Hankel and Toeplitz operators: continuous and discrete representations

Yafaev D. R.

Opuscula Mathematica

2017

Vol. 37, no. 1

189--218

We find a relation guaranteeing that Hankel operators realized in the space of sequences [formula] and in the space of functions [formula] are unitarily equivalent. This allows us to obtain exhaustive spectral results for two classes of unbounded Hankel operators in the space [formula] generalizing in different directions the classical Hilbert matrix. We also discuss a link between representations of Toeplitz operators in the spaces [formula] and [formula].