Differentiability of bizonal positive definite kernels on complex spheres

作者：Menegatto V A^*

来源：Journal of Mathematical Analysis and Applications, 2014, 412(1): 189-199.

DOI：10.1016/j.jmaa.2013.10.057

• Differentiability
• Positive definite kernels and functions
• Sphere
• Bizonal kernels

We prove that any continuous function with domain (z is an element of C: vertical bar z vertical bar <= 1) that generates a bizonal positive definite kernel on the unit sphere in C-q, q >= 3, is continuously differentiable in {z is an element of C: vertical bar z vertical bar < 1} up to order q - 2, with respect to both z and <(z)over bar>. In particular, the partial derivatives of the function with respect to x = Re z and y = Im z exist and are continuous in {z is an element of C: vertical bar z vertical bar < 1} up to the same order.

• 出版日期2014-4-1