A Unified View of Space–Time Covariance Functions Through Gelfand Pairs

Research output: Contribution to journal › Journal article › Research › peer-review

Standard

A Unified View of Space–Time Covariance Functions Through Gelfand Pairs. / Berg, Christian.

In: Journal of Fourier Analysis and Applications, Vol. 26, No. 6, 90, 2020.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Berg, C 2020, 'A Unified View of Space–Time Covariance Functions Through Gelfand Pairs', Journal of Fourier Analysis and Applications, vol. 26, no. 6, 90. https://doi.org/10.1007/s00041-020-09793-z

APA

Berg, C. (2020). A Unified View of Space–Time Covariance Functions Through Gelfand Pairs. Journal of Fourier Analysis and Applications, 26(6), [90]. https://doi.org/10.1007/s00041-020-09793-z

Vancouver

Berg C. A Unified View of Space–Time Covariance Functions Through Gelfand Pairs. Journal of Fourier Analysis and Applications. 2020;26(6). 90. https://doi.org/10.1007/s00041-020-09793-z

Author

Berg, Christian. / A Unified View of Space–Time Covariance Functions Through Gelfand Pairs. In: Journal of Fourier Analysis and Applications. 2020 ; Vol. 26, No. 6.

Bibtex

@article{ddadcad60aff47268688bc921420e3a0,
title = "A Unified View of Space–Time Covariance Functions Through Gelfand Pairs",
abstract = "We give a characterization of positive definite integrable functions on a product of two Gelfand pairs as an integral of positive definite functions on one of the Gelfand pairs with respect to the Plancherel measure on the dual of the other Gelfand pair. In the very special case where the Gelfand pairs are Euclidean groups and the compact subgroups are reduced to the identity, the characterization is a much cited result in spatio-temporal statistics due to Cressie, Huang and Gneiting. When one of the Gelfand pairs is compact the characterization leads to results about expansions in spherical functions with positive definite expansion functions, thereby recovering recent results of the author in collaboration with Peron and Porcu. In the special case when the compact Gelfand pair consists of orthogonal groups, the characterization is important in geostatistics and covers a recent result of Porcu and White.",
keywords = "Covariance functions, Harmonic analysis on Gelfand pairs, Positive definite functions",
author = "Christian Berg",
year = "2020",
doi = "10.1007/s00041-020-09793-z",
language = "English",
volume = "26",
journal = "Journal of Fourier Analysis and Applications",
issn = "1069-5869",
publisher = "Springer Basel AG",
number = "6",

}

RIS

TY - JOUR

T1 - A Unified View of Space–Time Covariance Functions Through Gelfand Pairs

AU - Berg, Christian

PY - 2020

Y1 - 2020

N2 - We give a characterization of positive definite integrable functions on a product of two Gelfand pairs as an integral of positive definite functions on one of the Gelfand pairs with respect to the Plancherel measure on the dual of the other Gelfand pair. In the very special case where the Gelfand pairs are Euclidean groups and the compact subgroups are reduced to the identity, the characterization is a much cited result in spatio-temporal statistics due to Cressie, Huang and Gneiting. When one of the Gelfand pairs is compact the characterization leads to results about expansions in spherical functions with positive definite expansion functions, thereby recovering recent results of the author in collaboration with Peron and Porcu. In the special case when the compact Gelfand pair consists of orthogonal groups, the characterization is important in geostatistics and covers a recent result of Porcu and White.

AB - We give a characterization of positive definite integrable functions on a product of two Gelfand pairs as an integral of positive definite functions on one of the Gelfand pairs with respect to the Plancherel measure on the dual of the other Gelfand pair. In the very special case where the Gelfand pairs are Euclidean groups and the compact subgroups are reduced to the identity, the characterization is a much cited result in spatio-temporal statistics due to Cressie, Huang and Gneiting. When one of the Gelfand pairs is compact the characterization leads to results about expansions in spherical functions with positive definite expansion functions, thereby recovering recent results of the author in collaboration with Peron and Porcu. In the special case when the compact Gelfand pair consists of orthogonal groups, the characterization is important in geostatistics and covers a recent result of Porcu and White.

KW - Covariance functions

KW - Harmonic analysis on Gelfand pairs

KW - Positive definite functions

UR - http://www.scopus.com/inward/record.url?scp=85096291696&partnerID=8YFLogxK

U2 - 10.1007/s00041-020-09793-z

DO - 10.1007/s00041-020-09793-z

M3 - Journal article

AN - SCOPUS:85096291696

VL - 26

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

SN - 1069-5869

IS - 6

M1 - 90

ER -

ID: 253134357