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arXiv · 2108.08830

Averaged mixed Julia-Fatou type theory with applications to spectral foliation

J. E. Pascoe·Ryan Tully-Doyle
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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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J. E. Pascoe, Ryan Tully-Doyle. 2021-08-19. Averaged mixed Julia-Fatou type theory with applications to spectral foliation. https://arxiv.org/abs/2108.08830

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