Positive definite kernels and integral operators generated by them

• Grant number: 14/00277-5
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2014
• End date: May 31, 2016
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valdir Antonio Menegatto
• Grantee: Valdir Antonio Menegatto
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Positive definite kernels and integral operators generated by them enter as important tools in the formulation of many problems in pure and applied mathematics. These problems intersect many research areas, including approximation theory, functional analysis, classical analysis, learning theory, etc. This proposal encompasses the resolution of problems aligned with the following topics: reproducing kernel Hilbert spaces, decay rates for eigenvalues of positive integral operators, differentiability of positive definite kernels, recovery of kernels via integration and characterization of some classes of positive definite kernels. The proposer has previous experience in these topics, which can be ratified by his many relevant publications in the area. (AU)

Scientific publications

(12)

(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)

GUELLA, J. C.; MENEGATTO, V. A.. Strictly positive definite kernels on a product of spheres. Journal of Mathematical Analysis and Applications, v. 435, n. 1, p. 286-301, MAR 1 2016. (12/22161-3, 14/00277-5)

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, OCT 2015. (14/06209-1, 14/00277-5)

BARBOSA, V. S.; MENEGATTO, V. A.. Differentiable positive definite functions on two-point homogeneous spaces. Journal of Mathematical Analysis and Applications, v. 434, n. 1, p. 698-712, FEB 1 2016. (14/00277-5)

GUELLA, J. C.; MENEGATTO, V. A.; PERON, A. P.. AN EXTENSION OF A THEOREM OF SCHOENBERG TO PRODUCTS OF SPHERES. Banach Journal of Mathematical Analysis, v. 10, n. 4, p. 671-685, OCT 2016. (12/22161-3, 14/25796-5, 14/00277-5)

GUELLA, JEAN C.; MENEGATTO, VALDIR A.; PERON, ARIA P.. Strictly Positive Definite Kernels on a Product of Spheres II. Symmetry Integrability and Geometry-Methods and Applications, v. 12, 2016. (16/03015-7, 14/25796-5, 14/00277-5)

BARBOSA, V. S.; MENEGATTO, V. A.. Strict positive definiteness on products of compact two-point homogeneous spaces. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, v. 28, n. 1, p. 56-73, JAN 2016. (14/00277-5)

BARBOSA, V. S.; MENEGATTO, V. A.. STRICTLY POSITIVE DEFINITE KERNELS ON COMPACT TWO-POINT HOMOGENEOUS SPACES. Mathematical Inequalities & Applications, v. 19, n. 2, p. 743-756, APR 2016. (14/00277-5)

AZEVEDO, D.; MENEGATTO, V. A.. Decay of Singular Values of Power Series Kernels on the Sphere. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION, v. 37, n. 4, p. 440-458, APR 2 2016. (10/00478-0, 14/00277-5)

GUELLA, J. C.; MENEGATTO, V. A.; PERON, A. P.. Strictly positive definite kernels on a product of circles. POSITIVITY, v. 21, n. 1, p. 329-342, MAR 2017. (12/22161-3, 14/25796-5, 14/00277-5)

GUELLA, J.; MENEGATTO, V. A.. Strictly Positive Definite Kernels on the Torus. CONSTRUCTIVE APPROXIMATION, v. 46, n. 2, p. 271-284, OCT 2017. (14/00277-5)

BONFIM, RAFAELA N.; MENEGATTO, VALDIR A.. Strict positive definiteness of multivariate covariance functions on compact two-point homogeneous spaces. JOURNAL OF MULTIVARIATE ANALYSIS, v. 152, p. 237-248, DEC 2016. (14/00277-5, 14/14380-2)

BARBOSA, VICTOR S.; MENEGATTO, VALDIR A.. Generalized Convolution Roots of Positive Definite Kernels on Complex Spheres. Symmetry Integrability and Geometry-Methods and Applications, v. 11, 2015. (14/00277-5)