Conditionally Positive Definite Matrix Valued Kernels on Euclidean Spaces
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Berg, C., Christensen, J.P.R., Ressel, P.: Harmonic Analysis on Semigroups. Theory of Positive Definite and Related Functions. Graduate Texts in Mathematics, vol. 100. Springer, New York (1984)
Berschneider, G., zu Castell, W., Schrödl, S.J.: Function spaces for conditionally positive definite operator-valued kernels. Math. Comput. 81(279), 1551–1569 (2012)
Buhmann, M.: Radial Basis Functions: Theory and Implementations. Cambridge University Press, Cambridge (2003)
Folland, G.B.: Real Analysis. Modern Techniques and Their Applications. Pure and Applied Mathematics, 2nd edn. Wiley, New York (1999)
Gelfand, I.M., Vilenkin, N.Y.: Generalized Functions, Volume 4: Applications of Harmonic Analysis. AMS Chelsea Publishing, New York (1964)
Gesztesy, F., Pang, M.: On (conditional) positive semidefiniteness in a matrix-valued context. Studia Math. 236(2), 143–192 (2017)
Guella, J.C., Menegatto, V.A., Porcu, E.: Strictly positive definite multivariate covariance functions on spheres. J. Multivar. Anal. 166, 150–159 (2018)
Guo, K., Hu, S., Sun, X.: Conditionally positive definite functions and Laplace–Stieltjes integrals. J. Approx. Theory 74(3), 249–265 (1993)
Horn, R.A., Johnson, C.R.: Topics in Matrix Analysis. Corrected Reprint of the 1991 Original. Cambridge University Press, Cambridge (1994)
Micchelli, C.A.: Interpolation of scattered data: distance matrices and conditionally positive definite functions. Constr. Approx. 2(11), 11–22 (1986)
Narcowich, F.J.: Generalized Hermite interpolation and positive definite kernels on a Riemannian manifold. J. Math. Anal. Appl. 190(1), 165–193 (1995)
Narcowich, F.J., Ward, J.D.: Generalized Hermite interpolation via matrix-valued conditionally positive definite functions. Math. Comput. 63(208), 661–687 (1994)
Schilling, R.L., Song, R., Vondracek, Z.: Bernstein Functions. Theory and Applications. De Gruyter Studies in Mathematics, vol. 37, 2nd edn. Walter de Gruyter & Co., Berlin (2012)
Sun, X.: Conditionally positive definite functions and their application to multivariate interpolations. J. Approx. Theory 74(2), 159–180 (1993)
Wang, R., Du, J., Ma, C.: Covariance matrix functions of isotropic vector random fields. Commun. Statist. Theory Methods 43(10–12), 2081–2093 (2014)
Wells, J.H., Williams, L.R.: Embeddings and Extensions in Analysis. Ergebnisse der Mathematik und ihrer Grenzgebiete Band 84. Springer, New York (1975)
Wendland, H.: Scattered Data Approximation. Cambridge University Press, Cambridge (2005)
Xie, T.: Positive definite matrix-valued functions and matrix variogram modeling. Thesis (Ph.D.), The University of Arizona (1994)