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In this chapter we explore how one can significantly generalize the classical Cesàro operator and open up many possibilities for future discovery. We focus on the Hardy space \(H^2\) and direct the reader to the endnotes for further results in other settings. Towards the end of this chapter we will survey how these generalized Cesàro operators came about and how they connect with our semigroup discussion from Chap. 8 .

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Generalized Cesàro Operators

  • 章节

  • 发表日期：

    2026年

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  • Javad Mashreghi,
  • William T. Ross

摘要

In this chapter we explore how one can significantly generalize the classical Cesàro operator and open up many possibilities for future discovery. We focus on the Hardy space \(H^2\) and direct the reader to the endnotes for further results in other settings. Towards the end of this chapter we will survey how these generalized Cesàro operators came about and how they connect with our semigroup discussion from Chap. 8 .