The Borel transform

  • Leon Ehrenpreis


We formulate the Borel transform in terms of functional analysis, in particular in terms of Analytically Uniform (AU) spaces. This enables us to extend the ideas of Borel to functions of several complex variables. Combining these ideas with nonlinear Fourier analysis leads to a generalization of the convexity that appears in Borel’s work.


Power Series Convex Hull Holomorphic Function Entire Function Analytic Continuation 
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Copyright information

© Springer 2008

Authors and Affiliations

  • Leon Ehrenpreis
    • 1
  1. 1.Temple UniversityUSA

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