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Analogue of slant Hankel operators on the Lebesgue space of n-torus

Abstract

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

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Correspondence to Bhawna Bansal Gupta.

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Communicated by Yuri Karlovich.

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Datt, G., Gupta, B.B. Analogue of slant Hankel operators on the Lebesgue space of n-torus. Adv. Oper. Theory 6, 66 (2021). https://doi.org/10.1007/s43036-021-00162-1

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Keywords

  • Hankel operator
  • kth-order slant Hankel operator
  • Lebesgue space
  • Slant Hankel operator
  • Slant Toeplitz operator

Mathematics Subject Classification

  • Primary 47B35
  • Secondary 46E30