The Borel transform

Leon Ehrenpreis
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Leon Ehrenpreis: Temple University

A chapter in Algebraic Analysis of Differential Equations, 2008, pp 119-131 from Springer

Abstract: Abstract 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.

Keywords: Power Series; Convex Hull; Holomorphic Function; Entire Function; Analytic Continuation (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-73240-2_12

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DOI: 10.1007/978-4-431-73240-2_12

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