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  • Author or Editor: G. Mastroianni x
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We generalize a theorem of Freud and Szabados [3] on one-sided polynomial approxi- mation in five different directions: we allow functions with exponential growth at infinity, Lp-metric, Freud-type weights instead of Hermite weights, functions with bounded deriva- tives instead of bounded variation, and include the momentum in the error estimate.

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Abstract  

In order to approximate functions defined on the real line or on the real semiaxis by polynomials, we introduce some new Fourier-type operators, connected to the Fourier sums of generalized Freud or Laguerre orthonormal systems. We prove necessary and sufficient conditions for the boundedness of these operators in suitable weighted L p-spaces, with 1 < p < ∞. Moreover, we give error estimates in weighted L p and uniform norms.

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Abstract  

In order to approximate functions defined on (0, +∞), the authors consider suitable Lagrange polynomials and show their convergence in weighted L p-spaces.

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Abstract  

We generalize Laguerre weights on R+ by multiplying them by translations of finitely many Freud type weights which have singularities, and prove polynomial approximation theorems in the corresponding weighted spaces.

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