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Analyticity of Higher-Order Moduli of Continuity of Real-Analytic Functions

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Abstract

The Perel'man's result according to which the first modulus of continuity of any real-analytic function f is a function analytic in a certain neighborhood of the origin is generalized to the case of arbitrary moduli of continuity of higher order.

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REFERENCES

  1. M. Ya. Perel'man, “On the modulus of continuity of analytic functio ns,” Uch. Zap. Leningr. Univ., Ser. Mat. Nauk, Issue 12, No. 83, 62-86 (1941).

    Google Scholar 

  2. A. A. Dovgoshei and L. L. Potemkina, “Conditions for analyticity of the modulus of continuity of piecewise-analytic functions,” Dopov. Nats. Akad. Nauk. Ukr., No. 7, 16-20 (2002).

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  3. A. A. Dovgoshei and L. L. Potemkina, “Modulus of continuity of piecewise-analytic functions,” Mat. Zametki, 73, No. 1, 63-76 (2003).

    Google Scholar 

  4. V. K. Dzyadyk, Introduction to the Theory of Uniform Polynomial Approximation of Functions [in Russian], Nauka, Moscow (1977).

    Google Scholar 

  5. I. A. Shevchuk, Polynomial Approximation and Traces of Functions Continuous on a Segment [in Russian], Naukova Dumka, Kiev (1992).

    Google Scholar 

  6. K. I. Babenko, Foundations of Numerical Analysis [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  7. R. P. Stanley, Enumerative Combinatorics [Russian translation], Mir, Moscow (1990).

  8. M. Abramowitz and I. A. Stegun (editors), Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, National Bureau of Standards, Appl. Math., Ser. 55 (1964).

  9. G. M. Fikhtengol'ts, A Course of Differential and Integral Calculus [in Russian], Vol. 1, Nauka, Moscow (1969).

    Google Scholar 

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Authors and Affiliations

  1. Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Donetsk

    A. A. Dovgoshei & L. L. Potemkina

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  1. A. A. Dovgoshei
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  2. L. L. Potemkina
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Dovgoshei, A.A., Potemkina, L.L. Analyticity of Higher-Order Moduli of Continuity of Real-Analytic Functions. Ukrainian Mathematical Journal 55, 905–920 (2003). https://doi.org/10.1023/B:UKMA.0000010592.27400.a1

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  • DOI: https://doi.org/10.1023/B:UKMA.0000010592.27400.a1

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