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Polynomial approximation with an exponential weight on the real semiaxis

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Abstract

We consider the polynomial approximation on (0,+∞), with the weight \(u(x)= x^{\gamma}e^{-x^{-\alpha}-x^{\beta}}\), α>0, β>1 and γ≧0. We introduce new moduli of smoothness and related K-functionals for functions defined on the real semiaxis, which can grow exponentially both at 0 and at +∞. Then we prove the Jackson theorem, also in its weaker form, and the Stechkin inequality. Moreover, we study the behavior of the derivatives of polynomials of best approximation.

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Authors and Affiliations

  1. Department of Mathematics, Computer Sciences and Economics, University of Basilicata, Via dell’Ateneo Lucano 10, 85100, Potenza, Italy

    Giuseppe Mastroianni & Incoronata Notarangelo

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  1. Giuseppe Mastroianni
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  2. Incoronata Notarangelo
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Correspondence to Giuseppe Mastroianni.

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The first author was partially supported by GNCS Project 2012 “Accoppiamento di metodi numerici per BIEs e PDEs relative a problemi evolutivi multistrato/esterni”. The second author acknowledges the support University of Basilicata (local funds).

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Mastroianni, G., Notarangelo, I. Polynomial approximation with an exponential weight on the real semiaxis. Acta Math Hung 142, 167–198 (2014). https://doi.org/10.1007/s10474-013-0348-2

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  • DOI: https://doi.org/10.1007/s10474-013-0348-2

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