Let S∞ denote the unit sphere in some infinite dimensional complex Hilbert space (H,<·,·>)Let z1,z2,…,z1 be distinct points on S∞ This paper deals with interpolation of arbitrary data on the zj by a...Let S∞ denote the unit sphere in some infinite dimensional complex Hilbert space (H,<·,·>)Let z1,z2,…,z1 be distinct points on S∞ This paper deals with interpolation of arbitrary data on the zj by a function in the linear span of the l functionswhen is a suitable function that operates on nonnegative definite matrices.Conditions for the strict positive definiteness of the kernel are obtained.展开更多
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 n...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 functions展开更多
文摘Let S∞ denote the unit sphere in some infinite dimensional complex Hilbert space (H,<·,·>)Let z1,z2,…,z1 be distinct points on S∞ This paper deals with interpolation of arbitrary data on the zj by a function in the linear span of the l functionswhen is a suitable function that operates on nonnegative definite matrices.Conditions for the strict positive definiteness of the kernel are obtained.
文摘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 functions
