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This chapter explores several semigroups of weighted composition operators on the Hardy space \(H^2\) associated with the Cesàro operator and its adjoint. Though this material is ascetically interesting in its own right, it is often used to discuss the boundedness and spectral properties of the Cesàro operator on other spaces of analytic functions on \(\mathbb {D}\) such as the Hardy spaces \(H^p\) , the Bergman spaces \(A^p\) , and certain Dirichlet type spaces. In Chap. 9 we will use this semigroup material to explore the invariant subspaces of the Cesàro operator on \(H^2\) .Bergman spaceDirichlet space

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The Cesàro Operator and Semigroups

  • 章节

  • 发表日期：

    2026年

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  • Javad Mashreghi,
  • William T. Ross

摘要

This chapter explores several semigroups of weighted composition operators on the Hardy space \(H^2\) associated with the Cesàro operator and its adjoint. Though this material is ascetically interesting in its own right, it is often used to discuss the boundedness and spectral properties of the Cesàro operator on other spaces of analytic functions on \(\mathbb {D}\) such as the Hardy spaces \(H^p\) , the Bergman spaces \(A^p\) , and certain Dirichlet type spaces. In Chap. 9 we will use this semigroup material to explore the invariant subspaces of the Cesàro operator on \(H^2\) .Bergman spaceDirichlet space