Averaged mixed Julia-Fatou type theory with applications to spectral foliation
J. E. Pascoe,
Ryan Tully-Doyle
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 nontangential 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 … Show more
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