In order to approximate functions defined on (-1,1) and having exponential singularities at the endpoints of the interval, we study the behavior of some modified Fourier Sums in an orthonormal system related to exponential weights. We give necessary and sufficient conditions for the boundedness of the related operators in suitable weighted Lp-spaces, with 1<∞. Then, in these spaces, these processes converge with the order of the best polynomial approximation. © 2011 Elsevier Inc.
Lp-convergence of Fourier sums with exponential weights on (-1,1)
Notarangelo I.
2011-01-01
Abstract
In order to approximate functions defined on (-1,1) and having exponential singularities at the endpoints of the interval, we study the behavior of some modified Fourier Sums in an orthonormal system related to exponential weights. We give necessary and sufficient conditions for the boundedness of the related operators in suitable weighted Lp-spaces, with 1<∞. Then, in these spaces, these processes converge with the order of the best polynomial approximation. © 2011 Elsevier Inc.
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