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This chapter covers two related Cesàro operators on \(L^2(0, 1)\) and \(L^2(0, \infty )\) called the continuous Cesàro operators.Continuous Cesàro operators They are lesser known, but more thoroughly understood, than the discrete Cesàro operator on \(\ell ^2\) covered in previous chapters of this book. For these two operators, we survey their norms, spectral properties, resolvent, invariant subspaces, and Fredholm theory. Along the way, we relate these two operators to the unilateral shift on \(H^2\) , the bilateral shift on \(L^2\) , and the classical Volterra operator on \(L^2(0, 1)\) .

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The Continuous Cesàro Operators

  • 章节

  • 发表日期：

    2026年

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  • Javad Mashreghi,
  • William T. Ross

摘要

This chapter covers two related Cesàro operators on \(L^2(0, 1)\) and \(L^2(0, \infty )\) called the continuous Cesàro operators.Continuous Cesàro operators They are lesser known, but more thoroughly understood, than the discrete Cesàro operator on \(\ell ^2\) covered in previous chapters of this book. For these two operators, we survey their norms, spectral properties, resolvent, invariant subspaces, and Fredholm theory. Along the way, we relate these two operators to the unilateral shift on \(H^2\) , the bilateral shift on \(L^2\) , and the classical Volterra operator on \(L^2(0, 1)\) .