Best approximations of integrals by integrals of finite rank

We investigate the quantities e σ ( f ) of the best approximation for integrals of functions from the spaces L p ( A , d μ ) by integrals of finite rank σ . We find exact values of these approximations in the case where the function f is a product of two nonnegative functions one of which is fixed a...

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Bibliographic Details
Published in:Journal of approximation theory 2010-02, Vol.162 (2), p.323-348
Main Authors: Stepanets, A.I., Shidlich, A.L.
Format: Article
Language:English
Subjects:
Best approximations
Function of exponential type
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Summary:We investigate the quantities e σ ( f ) of the best approximation for integrals of functions from the spaces L p ( A , d μ ) by integrals of finite rank σ . We find exact values of these approximations in the case where the function f is a product of two nonnegative functions one of which is fixed and the other varies on the unit ball U p ( A ) in the space L p ( A , d μ ) . We also consider applications of the obtained results to the approximation of periodic functions defined by convolutions with summable kernels by functions of exponential type.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2009.05.007