On Conditionally Positive Definite Dot Product Kernels  

作　　者：V.A.MENEGATTO C.P.OLIVEIRA Ana P.PERON 

机构地区：[1]Departamento de Matemática,ICMC-USP- Sāo Carlos,Caixa Postal 668,13560-970 Sāo Carlos SP,Brasil [2]Universidade Federal de Itajubá,ICE-DMC,Caixa Postal 50,37500-903 ItajubáMG,Brasil

出　　处：《Acta Mathematica Sinica,English Series》2008年第7期1127-1138,共12页数学学报（英文版）

基　　金：PROCAD-CAPES,Grant # 0092/01-0

摘　　要：Let m and n be fixed, positive integers and P a space composed of real polynomials in m variables. The authors study functions f ： R →R which map Gram matrices, based upon n points of R^m, into matrices, which are nonnegative definite with respect to P Among other things, the authors discuss continuity, differentiability, convexity, and convexity in the sense of Jensen, of such functionsLet m and n be fixed, positive integers and P a space composed of real polynomials in m variables. The authors study functions f ： R →R which map Gram matrices, based upon n points of R^m, into matrices, which are nonnegative definite with respect to P Among other things, the authors discuss continuity, differentiability, convexity, and convexity in the sense of Jensen, of such functions

关 键 词：conditionally positive definite kernels dot product kernels Gram matrices CONVEXITY convexity in the sense of Jensen 

分 类 号：O174[理学—数学]