@article{aada864fe61b4601a3eb558dcba4b6a1,
title = "Zastavnyi operators and positive definite radial functions",
abstract = "we consider a new operator acting on rescaled weighted differences between two members of the class Φd of positive definite radial functions. In particular, we study the positive definiteness of the operator for the Mat{\'e}rn, Generalized Cauchy and Wendland families.",
keywords = "Completely monotonic, Fourier transforms, Positive definite, Radial functions",
author = "Tarik Faouzi and Emilio Porcu and Moreno Bevilacqua and Igor Kondrashuk",
note = "Funding Information: The authors dedicate this work to Viktor Zastavnyi for his sixtieth birthday. Partial support was provided by Millennium Science Initiative of the Ministry of Economy, Development, and Tourism, Chile , grant “Millenium Nucleus Center for the Discovery of Structures in Complex Data” for Moreno Bevilacqua and Emilio Porcu, by FONDECYT grant 1160280 , Chile for Moreno Bevilacqua and by FONDECYT grant 1130647 , Chile for Emilio Porcu and by grant Diubb 170308 3/I from the university of Bio Bio, Chile for Tarik Faouzi. Tarik Faouzi and Igor Kondrashuk thank the support of project DIUBB 172409 GI/C at University of B{\'i}o-B{\'i}o, Chile . The work of I.K. was supported in part by Fondecyt (Chile) Grants No. 1121030 and by DIUBB (Chile) Grant No. 1814093/R . Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",
year = "2020",
month = feb,
doi = "10.1016/j.spl.2019.108620",
language = "British English",
volume = "157",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier",
}