@article{f2c3890957cc488e9f38b47f078d0f12,
title = "Buhmann covariance functions, their compact supports, and their smoothness",
abstract = "We consider the Buhmann class of radially symmetric and compactly supported covariance functions, that includes the most prominent classes used in both numerical analysis and spatial statistics literature. We discuss a very simple difference operator and report the conditions for which the application of it to Buhmann functions preserves positive definiteness on m-dimensional Euclidean spaces. We also show a relation between the Zastavnyi-Porcu problem [39] for Buhmann functions and a class of completely monotone functions.",
keywords = "Compact Support, Completely Monotonic, Fourier transforms, Laplace transforms",
author = "Emilio Porcu and Zastavnyi, {Viktor P.} and Moreno Bevilacqua",
note = "Funding Information: We are grateful to Professor R. Furrer for helpful remarks through the preparation of the manuscript. We are very grateful to the editor and to an anonymous referee for the thorough reviews that allowed for an improved version of the manuscript. Research work of Moreno Bevilacqua was partially supported by grant FONDECYT 1160280 from Chilean government. Research work of Emilio Porcu was partially supported by grant FONDECYT 1130647 from Chilean government. Publisher Copyright: {\textcopyright} 2017, Padova University Press. All rights reserved.",
year = "2017",
language = "English",
volume = "10",
pages = "33--42",
journal = "Dolomites Research Notes on Approximation",
issn = "2035-6803",
publisher = "University of Verona",
}