Omitted rays and wedges of fractional Cauchy transforms

Academic Article


  • AbstractFor α > 0 let α denote the set of functions which can be expressed where μ is a complex-valued Borel measure on the unit circle. We show that if f is an analytic function in Δ = {z ∈ : |z| < 1} and there are two nonparallel rays in /f(Δ) which do not meet, then fα where απ denotes the largest of the two angles determined by the rays. Also if the range of a function analytic in Δ is contained in an angular wedge of opening απ and 1 < α < 2, then fα.
  • Authors

  • Hibschweiler, Rita
  • MacGregor, TH
  • Status

    Publication Date

  • June 2006
  • Has Subject Area

    Digital Object Identifier (doi)

    Start Page

  • 367
  • End Page

  • 373
  • Volume

  • 80
  • Issue

  • 3