Title

On borel summability and analytic functionals

Document Type

Article

Publication Date

8-27-2013

Abstract

We show that a formal power series has positive radius of convergence if and only if it is uniformly Borel summable over a circle with center at the origin. Consequently, we obtain that an entire function f is of exponential type if and only if the formal power series Σn=0∞ f(n)(0)zn is uniformly Borel summable over a circle centered at the origin. We apply these results to obtain a characterization of those Silva tempered ultradistributions which are analytic functionals. We also use Borel summability to represent analytic functionals as Borel sums of their moment Taylor series over the Borel polygon. Copyright © 2013 Rocky Mountain Mathematics Consortium.

Publication Source (Journal or Book title)

Rocky Mountain Journal of Mathematics

First Page

895

Last Page

903

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