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Toeplitz matrices and operators, Toeplitz operators on l2(ℤ+).
The existence of the symbol, the discrete Hilbert transform.
The Hankel matrices and operators: the existence of the symbol (Nehari), compact and finite rank Hankel operators.
The Berezin transform, the Garsia norm, the spaces BMO, VMO, H∞ + C and QC, the compact commutators.