The Borel transform
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.
KeywordsPower Series Convex Hull Holomorphic Function Entire Function Analytic Continuation
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