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Analogue of slant Hankel operators on the Lebesgue space of n-torus. (English) Zbl 1523.47043

Summary: In this paper, the multivariate analogue of slant Hankel operator is introduced on \(L^2(\mathbb{T}^n)\), \(n\geq 1\) a natural number, the Lebesgue space of square integrable functions defined on \(\mathbb{T}^n\), where \(\mathbb{T}\) is the unit circle. Various characterizations are obtained for a bounded operator on \(L^2(\mathbb{T}^n)\) to be a \(k\)th-order slant Hankel operator, \(k\geq 2\) a fixed integer.

MSC:

47B35 Toeplitz operators, Hankel operators, Wiener-Hopf operators
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
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