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 J. Sib. Fed. Univ. Math. Phys., 2019, Volume 12, Issue 6, Pages 694–698 (Mi jsfu807)

On analytical complexity of antiderivatives

Maria A. Stepanova

Steklov Mathematical Institute RAS, Gubkina, 8, Moscow, 119991, Russia

Abstract: It is shown that the class of all functions of two variables of finite analytical complexity is not closed under integration. It also follows that the class of all functions of finite analytical complexity in the case of three or more variables is not closed under integration. For the case of three or more variables explicit examples of finite complexity functions with infinite complexity antiderivatives are constructed.

Keywords: analytical complexity, integration, finite complexity functions.

 Funding Agency Grant Number Russian Science Foundation 19-11-00316 This work is supported by the Russian Science Foundation under grant 19-11-00316.

DOI: https://doi.org/10.17516/1997-1397-2019-12-6-694-698

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Bibliographic databases:

UDC: 517.55, 512.628.2, 517.589
Accepted: 20.10.2019
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Citation: Maria A. Stepanova, “On analytical complexity of antiderivatives”, J. Sib. Fed. Univ. Math. Phys., 12:6 (2019), 694–698

Citation in format AMSBIB
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