@misc{10481/82258,
year = {2023},
url = {https://hdl.handle.net/10481/82258},
abstract = {In this work, we deal in a d dimensional unit ball equipped with an inner product
constructed by adding a mass point at zero to the classical ball inner product applied to
the gradients of the functions. Apart from determining an explicit orthogonal polynomial
basis, we study approximation properties of Fourier expansions in terms of this basis.
In particular, we deduce relations between the partial Fourier sums in terms of the
new orthogonal polynomials and the partial Fourier sums in terms of the classical ball
polynomials. We also give an estimate of the approximation error by polynomials of
degree at most n in the corresponding Sobolev space, proving that we can approximate
a function by using its gradient. Numerical examples are given to illustrate the
approximation behavior of the Sobolev basis.},
organization = {Ministerio de Ciencia, Innovacion y Universidades (MICINN), Spain	PGC2018-096504-B-C33},
organization = {Comunidad de Madrid},
organization = {Universidad Rey Juan Carlos, Spain	M2731},
organization = {FEDER/Junta de Andalucia, Spain	A-FQM-246-UGR20},
organization = {MCIN/AEI},
organization = {FEDER, Spain funds	PGC2018-094932-B-I00},
organization = {IMAG-Maria de Maeztu, Spain	CEX2020-001105-M},
publisher = {Elsevier},
keywords = {Approximation on the ball},
keywords = {Inner product via gradient},
keywords = {Fourier expansions},
title = {Approximation via gradients on the ball. The Zernike case},
doi = {10.1016/j.cam.2023.115258},
author = {Marriaga, Misael E. and Pérez Fernández, Teresa Encarnación and Piñar González, Miguel Ángel and Recarte, Marlon J.},
}