## Abstract

We prove that the singular numbers of the Cauchy transform {Mathematical expression} on L^{2}(D) are asymptotically {Mathematical expression}, while s_{n}(C_{|}L_{a}^{2}(D))≈1/n (where L_{a}^{2}(D) is the subspace of analytic functions in L^{2}(D)). Also, the singular numbers of the logarithmic potential {Mathematical expression} on L^{2}(D) are asympotically s_{n}(L)≈1/n, while s_{n}(L_{|La}^{2}(D))≈1/n^{2}. Our methods yield the asymptotic behavior of the singular numbers of the Cauchy Transform from L_{L}^{2}(μ) into L^{2}(ν) where μ and ν are rotation-invariant measures on {Mathematical expression}.

Original language | English |
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Pages (from-to) | 901-919 |

Number of pages | 19 |

Journal | Integral Equations and Operator Theory |

Volume | 15 |

Issue number | 6 |

DOIs | |

State | Published - Nov 1992 |

## Keywords

- AMS Classification Numbers: 47B10, 46E22

## ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory

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