Positive definite functions on spheres: the matricial and parametrical versions

• Grant number: 14/14380-2
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: September 01, 2014
• End date: July 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Agreement: Coordination of Improvement of Higher Education Personnel (CAPES)
• Principal Investigator: Valdir Antonio Menegatto
• Grantee: Rafaela Neves Bonfim
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

This project seeks characterizations for positive definite and stritcly positive definite isotropic matrix-valued functions on (real and complex) spheres and other manifolds, similar to the classical characterization obtained by I. J. Schoenberg in the forties for scalar positive definite and stritcly positive definite isotropic functions on spheres.\ In the strict case the investigation may consider connections between results involving different dimensions. The project also intends to cover a bifurcation into scalar positive definite and strictly positive definite functions on sphere that depend upon parameters, as previously investigated by O. Musin in the late nineties. (AU)

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)

BONFIM, RAFAELA N.; GUELLA, JEAN C.; MENEGATTO, VALDIR A.. Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative. Symmetry Integrability and Geometry-Methods and Applications, v. 14, 2018. (16/09906-0, 14/14380-2)

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)

Academic Publications

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

BONFIM, Rafaela Neves. Positive definite and isotropic kernels on compact two-point homogeneous spaces. 2017. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.