Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative
For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a similar characterization for kernels on the space-time setting G×S...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2018 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2018
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/209845 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative / R.N. Bonfim, J.C. Guella, V.A. Menegatto // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 29 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862672534490578944 |
|---|---|
| author | Bonfim, R.N. Guella, J.C. Menegatto, V.A. |
| author_facet | Bonfim, R.N. Guella, J.C. Menegatto, V.A. |
| citation_txt | Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative / R.N. Bonfim, J.C. Guella, V.A. Menegatto // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 29 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a similar characterization for kernels on the space-time setting G×Sᵈ, where G is a locally compact group, and Sᵈ is the unit sphere in ℝᵈ⁺¹, keeping isotropy of the kernels with respect to the Sᵈ component. Among other things, these results provide new procedures for the construction of valid models for interpolation and approximation on compact two-point homogeneous spaces.
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| first_indexed | 2025-12-07T15:36:11Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-209845 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:36:11Z |
| publishDate | 2018 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bonfim, R.N. Guella, J.C. Menegatto, V.A. 2025-11-27T14:50:20Z 2018 Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative / R.N. Bonfim, J.C. Guella, V.A. Menegatto // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 29 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 33C45; 42A82; 42C10; 43A35 arXiv: 1803.03105 https://nasplib.isofts.kiev.ua/handle/123456789/209845 https://doi.org/10.3842/SIGMA.2018.112 For two continuous and isotropic positive definite kernels on the same compact two-point homogeneous space, we determine necessary and sufficient conditions in order that their product be strictly positive definite. We also provide a similar characterization for kernels on the space-time setting G×Sᵈ, where G is a locally compact group, and Sᵈ is the unit sphere in ℝᵈ⁺¹, keeping isotropy of the kernels with respect to the Sᵈ component. Among other things, these results provide new procedures for the construction of valid models for interpolation and approximation on compact two-point homogeneous spaces. The first and third authors acknowledge partial financial support from FAPESP, grants #2014/14380-2 and 2016/09906-0. Likewise, the second one acknowledges partial financial support from PROEX-CAPES. The authors would like to express their gratitude to the anonymous referees for their valuable suggestions on the original manuscript. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative Article published earlier |
| spellingShingle | Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative Bonfim, R.N. Guella, J.C. Menegatto, V.A. |
| title | Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative |
| title_full | Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative |
| title_fullStr | Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative |
| title_full_unstemmed | Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative |
| title_short | Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative |
| title_sort | strictly positive definite functions on compact two-point homogeneous spaces: the product alternative |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/209845 |
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