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Analytic complexity of functions of several variables

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Abstract

An approach to estimating the complexity of analytic functions of arbitrarily many variables is proposed. A description of harmonic functions of complexity one of three variables and of algebraic functions of complexity one of arbitrarily many variables is given.

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References

  1. V. K. Beloshapka, “Analytic complexity of functions of two variables,” Russ. J. Math. Phys. 14 (3), 243–249 (2007).

    Article  MathSciNet  MATH  Google Scholar 

  2. V. K. Beloshapka, “A seven-dimensional family of simple harmonic functions,” Mat. Zametki 98 (6), 803–808 (2015) [Math. Notes 98 (5–6), 867–871 (2015)].

    Article  MathSciNet  MATH  Google Scholar 

  3. M. Stepanova, “On rational functions of first-class complexity,” Russ. J. Math. Phys. 23 (2), 251–256 (2016).

    Article  MathSciNet  MATH  Google Scholar 

  4. M. B. Villarino, Algebraic Addition Theorems, http://arxiv. org/abs/1212. 6471 (2013).

    Google Scholar 

  5. V. V. Prasolov and Yu. P. Solov’ev, Elliptic Functions and Algebraic Equations (Faktorial, Moscow, 1997; V. Prasolov and Yu. Solovyev, Elliptic Functions and Elliptic Integrals, Translations of Mathematical Monographs, 170. AMS, Providence, RI, 1997).

    Google Scholar 

  6. V. K. Beloshapka, “Algebraic functions of complexity one, a Weierstrass theorem, and three arithmetic operations,” Russ. J. Math. Phys. 23 (3), 343–347 (2016).

    Article  MathSciNet  Google Scholar 

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Correspondence to V. K. Beloshapka.

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Original Russian Text © V. K. Beloshapka, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 6, pp. 781–789.

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Beloshapka, V.K. Analytic complexity of functions of several variables. Math Notes 100, 774–780 (2016). https://doi.org/10.1134/S000143461611016X

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  • DOI: https://doi.org/10.1134/S000143461611016X

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