Mathematical Geosciences

, Volume 47, Issue 6, pp 699–717 | Cite as

Isotropic Covariance Matrix Functions On All Spheres

  • Chunsheng MaEmail author


This paper reviews and introduces characterizations of the covariance function on all spheres that is isotropic and continuous, and characterizations of the covariance matrix function on all spheres whose entries are isotropic and continuous. These characterizations are used to derive some covariance (matrix) structures on all spheres, with certain polynomials obtained, besides some rational, (negative) power, and logarithmic models.


Absolutely monotone function Covariance Cross covariance  Direct covariance Elliptically contoured random field Gaussian random field  Positive definite matrix 



This work was supported in part by U.S. Department of Energy under Grant DE-SC0005359. The author wishes to thank the reviewers for the valuable comments and suggestions which helped to improve the presentation of this paper tremendously.


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Copyright information

© International Association for Mathematical Geosciences 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Statistics, and PhysicsWichita State UniversityWichitaUSA
  2. 2.School of Mathematics and StatisticsHubei Engineering UniversityXiaoganChina

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