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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Mastroianni, G., Notarangelo, I. Some Fourier-type operators for functions on unbounded intervals. Acta Math Hung 127, 347–375 (2010). https://doi.org/10.1007/s10474-010-9137-3
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DOI: https://doi.org/10.1007/s10474-010-9137-3