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 Lp-spaces, with 1 < p < ∞. Moreover, we give error estimates in weighted Lp and uniform norms. © Akadémiai Kiadó, Budapest 2010.
Some Fourier-type operators for functions on unbounded intervals
Notarangelo I.
2010-01-01
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 Lp-spaces, with 1 < p < ∞. Moreover, we give error estimates in weighted Lp and uniform norms. © Akadémiai Kiadó, Budapest 2010.
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