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Article overview
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On Borel summability and analytic functionals | Ricardo Estrada
; Jasson Vindas
; | Date: |
19 Jun 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 $sum_{n=0}^{infty}f^{(n)}(0)z^{n}$ is
uniformly Borel summable over a circle centered a 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. | Source: | arXiv, 1306.4559 | Services: | Forum | Review | PDF | Favorites |
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