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Preprint
Averaged mixed Julia-Fatou type theory with applications to spectral foliation
arXiv.org
19 Aug 2021
Abstract
Classically, theorems of Fatou and Julia describe the boundary regularity of
functions in one complex variable. The former says that a complex analytic
function on the disk has non-tangential boundary values almost everywhere, and
the latter describes when a function takes an extreme value at a boundary point
and is differentiable there non-tangentially. We describe a class of
intermediate theorems in terms of averaged Julia-Fatou quotients. Boundary
regularity is related to integrability of certain quantities against a special
measure, the so-called Nevanlinna measure. Applications are given to spectral
theory.
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Details
- Title
- Averaged mixed Julia-Fatou type theory with applications to spectral foliation
- Creators
- J. E PascoeRyan Tully-Doyle
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021880196404721