On Compactly Supported Strictly Positive Definite Functions on the Sphere
by
Andrei Reztsov
School of Mathematics, The University of New South Wales, Sydney, Australia
Coauthors: Prof Ian Sloan, Dr Michael Hirschhorn

Several examples of compactly supported positive definite functions on the sphere  S²  were considered. As it was mentioned in recent paper by N. Dyn, F. Narkowich and J. Ward such functions could be constructed as a restriction to the sphere of compactly supported radial basis functions on m-dimensional Euclidean space,  m >= 4 . As a initial functions (for this restriction) we considered the modification of Wendland's functions. Some ideas of the paper mentioned above and ideas of R. Schaback and H. Wendland helped us to find the restriction of the modified Wendland's function from 3-dimensional Euclidean space that is STRICTLY positive definite.

Date received: February 9, 1999