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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

Full text: PDF file (91 kB)
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Bibliographic databases:

UDC: 517.55, 512.628.2, 517.589
Received: 29.07.2019
Received in revised form: 04.09.2019
Accepted: 20.10.2019
Language:

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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\by Maria~A.~Stepanova
\paper On analytical complexity of antiderivatives
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2019
\vol 12
\issue 6
\pages 694--698
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\crossref{https://doi.org/10.17516/1997-1397-2019-12-6-694-698}
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