Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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PROPERTIES OF kth-ORDER (SLANT TOEPLITZ + SLANT HANKEL) OPERATORS ON H2(𝕋)

  • Gupta, Anuradha (Department of Mathematics Delhi College of Arts and Commerce Netaji Nagar, University of Delhi) ;
  • Gupta, Bhawna (Department of Mathematics University of Delhi)
  • Received : 2019.11.22
  • Accepted : 2020.01.16
  • Published : 2020.07.31
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Abstract

For two essentially bounded Lebesgue measurable functions 𝜙 and ξ on unit circle 𝕋, we attempt to study properties of operators $S^k_{\mathcal{M}({\phi},{\xi})=S^k_{T_{\phi}}+S^k_{H_{\xi}}$ on H2(𝕋) (k ≥ 2), where $S^k_{T_{\phi}}$ is a kth-order slant Toeplitz operator with symbol 𝜙 and $S^k_{H_{\xi}}$ is a kth-order slant Hankel operator with symbol ξ. The spectral properties of operators Sk𝓜(𝜙,𝜙) (or simply Sk𝓜(𝜙)) are investigated on H2(𝕋). More precisely, it is proved that for k = 2, the Coburn's type theorem holds for Sk𝓜(𝜙). The conditions under which operators Sk𝓜(𝜙) commute are also explored.

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References

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