Positive Definite Functions on Complex Spheres and their Walks through Dimensions

Autor(es)

Massa, Eugenio ^[1] ; Peron, Ana Paula ^[1] ; Porcu, Emilio ^{[2, 3]}

Afiliação do(s) autor(es)

^[1] ICMC USP Sao Carlos, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Newcastle, Chair Spatial Analyt Methods, Sch Math & Stat, Callaghan, NSW - Australia

^[3] Univ Tecn Federico Santa Maria, Dept Math, Ave Espana 1680, Valparaiso 230123 - Chile

• Tipo de documento: Artigo Científico
• Fonte: Symmetry Integrability and Geometry-Methods and Applications; v. 13, 2017.
• Citações Web of Science: 3

Resumo

We provide walks through dimensions for isotropic positive definite functions defined over complex spheres. We show that the analogues of Montee and Descente operators as proposed by Beatson and zu Castell {[}J. Approx. Theory 2 2 1 (2017), 22-37] on the basis of the original Matheron operator {[}Les variables regionalisees et leur estimation, Masson, Paris, 1965], allow for similar walks through dimensions. We show that the Montee operators also preserve, up to a constant, strict positive definiteness. For the Descente operators, we show that strict positive definiteness is preserved under some additional conditions, but we provide counterexamples showing that this is not true in general. We also provide a list of parametric families of (strictly) positive definite functions over complex spheres, which are important for several applications. (AU)

• Processo FAPESP: 14/25398-0 - Equações e sistemas elípticos com vários tipos de interação com o espectro
• Beneficiário: Eugenio Tommaso Massa
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 14/25796-5 - Positividade (estrita) definida e diferenciabilidade
• Beneficiário: Ana Paula Peron
• Modalidade de apoio: Auxílio à Pesquisa - Regular
• Processo FAPESP: 16/03015-7 - Funções positivas definidas
• Beneficiário: Ana Paula Peron
• Modalidade de apoio: Bolsas no Exterior - Pesquisa