Decay rates for eigenvalues of positive integral operators on the sphere.

• Grant number: 10/00478-0
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: June 01, 2010
• End date: February 28, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Valdir Antonio Menegatto
• Grantee: Douglas Azevedo Sant 'Anna
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Este projeto tem como objetivo principal a obtenção de taxas de decaimento para autovalores de operadores integrais positivos sobre L^2(S^m), onde S^m é a esfera unitária m-dimensional.Diferentemente do que se encontra na literatura, as hipóteses básicas serão colocadas sobre os coeficientes na expansão monomial do núcleo. Precisamente, buscaremos resultados que descrevam o decaimento dos autovalores do operador integral em função de algum decaimento dos coeficientes na expansão do núcleo gerador.

Scientific publications

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

AZEVEDO, D.; MENEGATTO, V. A.. Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere. Journal of Approximation Theory, v. 177, p. 57-68, JAN 2014. (10/00478-0, 10/19734-6)

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)

AZEVEDO, D.; MENEGATTO, V. A.. EIGENVALUE DECAY OF INTEGRAL OPERATORS GENERATED BY POWER SERIES-LIKE KERNELS. Mathematical Inequalities & Applications, v. 17, n. 2, p. 693-705, APR 2014. (10/00478-0, 10/19734-6)

Academic Publications

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

'ANNA, Douglas Azevedo Sant. Eigenvalue decay of integral operators generated by power series. 2013. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.