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Fourier coefficients, K-functionals and applications


In this project it is intended, mainly, two targets described in the box bellow. Results related to the first one has turned out extremely efficient in the study of decay rates of eigenvalues of integral operators generated by smooth kernels on the sphere.Related to second target, such characterizations are highly important in Approximation Theory, where one of the most important problem is to feature the best approximation of a function by more simple functions (in the meaning of smoothness). This kind of characterization has its version for functions defined on the euclidian space and it employed spherical mean operator and Riesz-Bochner means. However, on the spherical setting is still an open problem. (AU)

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Scientific publications
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
JORDAO, T.; MENEGATTO, V. A.. JACKSON KERNELS: A TOOL FOR ANALYSING THE DECAY OF EIGENVALUE SEQUENCES OF INTEGRAL OPERATORS ON THE SPHERE. Mathematical Inequalities & Applications, v. 18, n. 4, p. 1483-1500, . (14/00277-5, 14/06209-1)
JORDAO, T.; MENEGATTO, V. A.. ESTIMATES FOR FOURIER SUMS AND EIGENVALUES OF INTEGRAL OPERATORS VIA MULTIPLIERS ON THE SPHERE. Proceedings of the American Mathematical Society, v. 144, n. 1, p. 269-283, . (11/21300-7, 14/06209-1)

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