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The reciprocal of a Borel summable function is Borel summable

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Abstract

It is proven that if a functionF is Borel summable in some angular region and has a non-vanishing derivative at the origin, then its reciprocalF −1 is also Borel summable in a region which has essentially the same angular extent.

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Authors and Affiliations

  1. Departement de Physique Mathématique, U.S.T.L., F-34060, Montpellier Cedex, France

    G. Auberson & G. Mennessier

Authors
  1. G. Auberson
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  2. G. Mennessier
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Communicated by H. Araki

Physique Mathématique et Théorique, Unité associée au CNRS No. 768

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Auberson, G., Mennessier, G. The reciprocal of a Borel summable function is Borel summable. Commun.Math. Phys. 100, 439–446 (1985). https://doi.org/10.1007/BF01206138

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  • DOI: https://doi.org/10.1007/BF01206138

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