On positive definiteness of some radial functions
- Authors: Zastavnyi V.P.1, Porcu E.2
-
Affiliations:
- Faculty of Mathematics and Information Technology
- Departamento de Matemática
- Issue: Vol 38, No 2 (2017)
- Pages: 386-394
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/199161
- DOI: https://doi.org/10.1134/S1995080217020226
- ID: 199161
Cite item
Abstract
We consider the functions hμ,ν introduced by Zastavnyi in 2002. The family of these functions is a subfamily of Buhmann’s functions and contains the families of functions introduced by Trigub in 1987 and Wendland in 1995. We investigate the problems of positive definiteness and smoothness at zero for the linear combinations β2εhμ,ν (x/β2) − β1εμ,ν (x/β1).
About the authors
V. P. Zastavnyi
Faculty of Mathematics and Information Technology
Author for correspondence.
Email: zastavn@rambler.ru
Ukraine, Universitetskaya ul. 24, Donetsk, 83001
E. Porcu
Departamento de Matemática
Email: zastavn@rambler.ru
Chile, Valparaiso