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On Borel summability and analytic functionals

Ricardo Estrada and Jasson Vindas Diaz UGent (2013) ROCKY MOUNTAIN JOURNAL OF MATHEMATICS. 43(3). p.895-903
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.
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Analytic functionals, Entire functions of exponential type, Borel summability, Borel polygon, Silva tempered ultradistributions
journal title
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
Rocky Mt. J. Math.
volume
43
issue
3
pages
895 - 903
Web of Science type
Article
Web of Science id
000322719800010
JCR category
MATHEMATICS
JCR impact factor
0.491 (2013)
JCR rank
191/302 (2013)
JCR quartile
3 (2013)
ISSN
0035-7596
DOI
10.1216/RMJ-2013-43-3-895
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
4115876
handle
http://hdl.handle.net/1854/LU-4115876
alternative location
http://projecteuclid.org/euclid.rmjm/1375361979
date created
2013-08-14 13:39:39
date last changed
2016-12-19 15:46:03
@article{4115876,
  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 \${\textbackslash}sum\_\{n=0\}\^{ }\{{\textbackslash}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.},
  author       = {Estrada, Ricardo and Vindas Diaz, Jasson},
  issn         = {0035-7596},
  journal      = {ROCKY MOUNTAIN JOURNAL OF MATHEMATICS},
  keyword      = {Analytic functionals,Entire functions of exponential type,Borel summability,Borel polygon,Silva tempered ultradistributions},
  language     = {eng},
  number       = {3},
  pages        = {895--903},
  title        = {On Borel summability and analytic functionals},
  url          = {http://dx.doi.org/10.1216/RMJ-2013-43-3-895},
  volume       = {43},
  year         = {2013},
}

Chicago
Estrada, Ricardo, and Jasson Vindas Diaz. 2013. “On Borel Summability and Analytic Functionals.” Rocky Mountain Journal of Mathematics 43 (3): 895–903.
APA
Estrada, R., & Vindas Diaz, J. (2013). On Borel summability and analytic functionals. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 43(3), 895–903.
Vancouver
1.
Estrada R, Vindas Diaz J. On Borel summability and analytic functionals. ROCKY MOUNTAIN JOURNAL OF MATHEMATICS. 2013;43(3):895–903.
MLA
Estrada, Ricardo, and Jasson Vindas Diaz. “On Borel Summability and Analytic Functionals.” ROCKY MOUNTAIN JOURNAL OF MATHEMATICS 43.3 (2013): 895–903. Print.