On functions of finite analytical complexity
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M. A. Stepanova;
Translated by: Anastasia Frantsuzova - Trans. Moscow Math. Soc. 2022, 1-13
- DOI: https://doi.org/10.1090/mosc/342
- Published electronically: September 23, 2024
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Abstract:
We construct examples of polynomials and analytic functions of any predetermined finite analytical complexity $n$. We obtain an estimate of the order of derivative of the differential-algebraic criteria for membership in the class $Cl_{n}$ of functions of analytical complexity not higher than $n$. We find uniform estimates for finite values $d_{n}$ of the analytic spectrum $\{d_{n}\}$ for systems of differential-algebraic equations of fixed order of derivative $\delta$.References
- V. I. Arnol′d, On the representation of continuous functions of three variables by superpositions of continuous functions of two variables, Mat. Sb. (N.S.) 48(90) (1959), 3–74 (Russian). MR 121453
- V. K. Beloshapka, Analytic complexity of functions of two variables, Russ. J. Math. Phys. 14 (2007), no. 3, 243–249. MR 2341772, DOI 10.1134/S1061920807030016
- V. K. Beloshapka, Analytical complexity: development of the topic, Russ. J. Math. Phys. 19 (2012), no. 4, 428–439. MR 3001077, DOI 10.1134/S1061920812040036
- V. K. Beloshapka, A seven-dimensional family of simple harmonic functions, Mat. Zametki 98 (2015), no. 6, 803–808 (Russian, with Russian summary); English transl., Math. Notes 98 (2015), no. 5-6, 867–871. MR 3438536, DOI 10.4213/mzm10865
- V. K. Beloshapka, Simple solutions of three equations of mathematical physics, Trans. Moscow Math. Soc. 79 (2018), 187–200. MR 3881464, DOI 10.1090/mosc/280
- V. K. Beloshapka, On simple solutions of some equations of mathematical physics, Russ. J. Math. Phys. 27 (2020), no. 3, 309–325. MR 4145902, DOI 10.1134/S1061920820030036
- A. N. Kolmogorov, On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition, Dokl. Akad. Nauk SSSR 114 (1957), 953–956 (Russian). MR 111809
- Alexander Ostrowski, Über Dirichletsche Reihen und algebraische Differentialgleichungen, Math. Z. 8 (1920), no. 3-4, 241–298 (German). MR 1544442, DOI 10.1007/BF01206530
- H. Poincaré, Les fonctions analytiques de deux variables et la représentation conforme, Rend. Circ. Mat. Palermo (2) 23 (1907), 185–220.
Bibliographic Information
- M. A. Stepanova
- Affiliation: Steklov Institute of Mathematics, Russian Academy of Sciences, Russia
- Email: step_masha@mail.ru
- Published electronically: September 23, 2024
- Additional Notes: This study was supported by a grant from the Russian Science Foundation (project No. 19-11-00316).
- © Copyright 2024 American Mathematical Society
- Journal: Trans. Moscow Math. Soc. 2022, 1-13
- MSC (2020): Primary 32A10
- DOI: https://doi.org/10.1090/mosc/342