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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

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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.

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Authors and Affiliations

  1. Institute of Mathematics, Ukrainian Academy of Sciences, Kyiv

    O. I. Stepanets’ & I. V. Sokolenko

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  1. O. I. Stepanets’
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  2. I. V. Sokolenko
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 56, No. 7, pp. 960–965, July, 2004.

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Stepanets’, O.I., Sokolenko, I.V. 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. Ukr Math J 56, 1144–1150 (2004). https://doi.org/10.1007/PL00022190

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  • DOI: https://doi.org/10.1007/PL00022190

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