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Toeplitz Operators on the Weighted Pluriharmonic Bergman Space with Radial Symbols

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  • Zhi Ling Sun
  • Yu Feng Lu

Abstract

We construct an operator ð ‘… whose restriction onto weighted pluriharmonic Bergman Space ð ‘ 2 𠜇 ( ð ”¹ ð ‘› ) is an isometric isomorphism between ð ‘ 2 𠜇 ( ð ”¹ ð ‘› ) and ð ‘™ # 2 . Furthermore, using the operator ð ‘… we prove that each Toeplitz operator 𠑇 ð ‘Ž with radial symbols is unitary to the multication operator ð ›¾ a , 𠜇 I . Meanwhile, the Wick function of a Toeplitz operator with radial symbol gives complete information about the operator, providing its spectral decomposition.

Suggested Citation

  • Zhi Ling Sun & Yu Feng Lu, 2011. "Toeplitz Operators on the Weighted Pluriharmonic Bergman Space with Radial Symbols," Abstract and Applied Analysis, Hindawi, vol. 2011, pages 1-15, September.
    • Handle: RePEc:hin:jnlaaa:210596
    DOI: 10.1155/2011/210596
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    Cited by:

    1. Zhi-Ling Sun & Wei-Shih Du & Feng Qi, 2024. "Toeplitz Operators on Harmonic Fock Spaces with Radial Symbols," Mathematics, MDPI, vol. 12(4), pages 1-12, February.

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