Strictly positive definite kernels on the sphere: an analysis of the recent results.

• Grant number: 12/22161-3
• Support Opportunities: Scholarships in Brazil - Master
• Start date: March 01, 2013
• End date: February 28, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valdir Antonio Menegatto
• Grantee: Jean Carlo Guella
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project is intended to address the analysis of some recent results on positive definite and bizonal kernels on the usual m-dimensional unit sphere. The analysis seeks a possible application in the characterization of those positive definite and bizonal kernels which are strictly positive definite of some fixed order. Actually, as some characterizations are already available, the main goal of the project is to verify if the latest techniques that appeared in the literature are enough to determine the remaining classes of strictly positive definite kernels. Along the way, we intend to consider some Pólya criterion for positive and strict positive definineteness recently described in the literature.

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)

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)

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, 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)

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

GUELLA, Jean Carlo. The Polya criterion on the sphere. 2015. Master's Dissertation - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.