Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative

Autor(es)

Bonfim, Rafaela N. ^[1] ; Guella, Jean C. ^[2] ; Menegatto, Valdir A. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Fed Sao Joao Del Rei, DEMAT, Praca Frei Orlando 170, BR-36307352 Sao Joao Del Rei, MG - Brazil

^[2] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Symmetry Integrability and Geometry-Methods and Applications; v. 14, 2018.
• Citações Web of Science: 0

Resumo

For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a similar characterization for kernels on the space-time setting G x S-d, where G is a locally compact group and S-d is the unit sphere in Rd+1, keeping isotropy of the kernels with respect to the S-d component. Among other things, these results provide new procedures for the construction of valid models for interpolation and approximation on compact two-point homogeneous spaces. (AU)

• Processo FAPESP: 16/09906-0 - Análise harmônica, teoria da aproximação, funções especiais e aplicações
• Beneficiário: Dimitar Kolev Dimitrov
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 14/14380-2 - Núcleos positivos definidos em esferas: versões matriciais e com parâmetros
• Beneficiário: Rafaela Neves Bonfim
• Modalidade de apoio: Bolsas no Brasil - Doutorado