Abstract
An extension of slant Hankel operator, namely, the k-th-order λ-slant Hankel operator on the Lebesgue space \(L^{2}(\mathbb{T}^{n})\), where \(\mathbb{T}\) is the unit circle and n ≥ 1, a natural number, is described in terms of the solution of a system of operator equations, which is subsequently expressed in terms of the product of a slant Hankel operator and a unitary operator. The study is further lifted in Calkin algebra in terms of essentially k-th-order λ-slant Hankel operators on \(L^{2}(\mathbb{T}^{n})\).
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Datt, G., Gupta, B.B. Operator Equations Inducing Some Generalizations of Slant Hankel Operators. Acta. Math. Sin.-English Ser. (2024). https://doi.org/10.1007/s10114-024-3084-3
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DOI: https://doi.org/10.1007/s10114-024-3084-3
Keywords
- Hankel operator
- Lebesgue space of n-dimensional torus
- k-th-order slant Hankel operator
- essentially k-th-order λ-slant Hankel operator