Advertisement

Ukrainian Mathematical Journal

, Volume 56, Issue 7, pp 1144–1150 | Cite as

Approximation of the <InlineEquation ID=”IE1”> <EquationSource Format=”MATHTYPE”> <![CDATA[ % MathType!MTEF!2!1!+- % feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D % aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq % Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq % Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaru % WvHjNBVn2AGaLCVbctPDgA0bYu1jgALfgzaGqbaiqa-H6agaqeaaaa % !42E4! ]]></EquationSource> <EquationSource Format=”TEX”> <![CDATA[$$ \bar \Psi $$]]></EquationSource></InlineEquation>-integrals of functions defined on the real axis by fourier operators

  • O. I. Stepanets’
  • I. V. Sokolenko
Article
  • 14 Downloads

Abstract

We find asymptotic formulas for the least upper bounds of the deviations of Fourier operators on classes of functions locally summable on the entire real axis and defined by <InlineEquation ID=”IE2”><EquationSource Format=”MATHTYPE”><![CDATA[% MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbnrfifHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaq% Fr0xc9pk0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qq% Q8frFve9Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaru% WvHjNBVn2AGaLCVbctPDgA0bYu1jgALfgzaGqbaiqa-H6agaqeaaaa% !42E4!]]></EquationSource><EquationSource Format=”TEX”><![CDATA[$$\bar \Psi $$]]></EquationSource></InlineEquation>-integrals. On these classes, we also obtain asymptotic equalities for the upper bounds of functionals that characterize the simultaneous approximation of several functions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    Stepanets, A. I. 2002Methods of Approximation TheoryInstitute of Mathematics, Ukrainian Academy of SciencesKievin RussianGoogle Scholar
  2. 2.
    Stepanets, A. I. 2002Methods of Approximation TheoryInstitute of Mathematics, Ukrainian Academy of SciencesKievin RussianGoogle Scholar
  3. 3.
    Stepanets, A. I. 1988Approximation of functions defined on the real axis by Fourier operatorsDokl. Akad. Nauk SSSR3035053Google Scholar
  4. 4.
    Stepanets, A. I. 1988Approximation of functions defined on the real axis by Fourier operatorsUkr. Mat. Zh.40198209Google Scholar
  5. 5.
    Stepanets, A. I. 1990Classes of functions defined on the real axis and their approximation by entire functions. IUkr. Mat. Zh.42102112Google Scholar
  6. 6.
    Stepanets, A. I. 1990Classes of functions defined on the real axis and their approximation by entire functions. IIUkr. Mat. Zh.42210222Google Scholar
  7. 7.
    Stepanets, A. I. 1994Approximation in the spaces of locally integrable functionsUkr. Mat. Zh.46597625Google Scholar
  8. 8.
    Stepanets, A. I., Kunyang, W., Xirong, Z. 1999Approximation of locally integrable functions on the real lineUkr. Mat. Zh.5115491561Google Scholar
  9. 9.
    Stepanets, A. I., Drozd, V. V. 1989Simultaneous approximation of functions and their derivatives by Fourier operators in the uniform metricSimultaneous Approximation of Functions and Their Derivatives by Fourier OperatorsInstitute of Mathematics, Ukrainian Academy of SciencesKievin RussianGoogle Scholar
  10. 10.
    Drozd, V. V. 1989Simultaneous approximation of functions and their derivatives by Fourier operatorsHarmonic Analysis and Development of Approximation MethodsInstitute of Mathematics, Ukrainian Academy of SciencesKiev5567in RussianGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2004

Authors and Affiliations

  • O. I. Stepanets’
    • 1
  • I. V. Sokolenko
    • 1
  1. 1.Institute of MathematicsUkrainian Academy of SciencesKyiv

Personalised recommendations