Orthonormal polynomials with generalized Freud-type weights

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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“…and, according to the Remez-type inequality (4.3), considering the subset [3]), the other ones being similar. By…”

Section: Proofsmentioning

confidence: 84%

Some Fourier-type operators for functions on unbounded intervals

Mastroianni

Notarangelo

2010

Acta Math Hung

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“…These polynomials, sometimes called generalized Freud polynomials, have been extensively studied in [5,13,28,6,7].…”

Section: Basic Factsmentioning

confidence: 99%

A Lagrange-type projector on the real line

Mastroianni

Notarangelo

2010

Math. Comp.

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“…These estimates can be deduced from the analogous ones in [12] with a change of variable (see also [13]). For the Christoffel numbers λ k , k = 1, .…”

Section: Orthogonal Polynomialsmentioning

confidence: 99%