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Strictly Positive Definite Kernels on a Product of Spheres II
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2016, том 12
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Strictly Positive Definite Kernels on a Product of Spheres II
Інший ID:
2010 Mathematics Subject Classification: 33C50; 33C55; 42A16; 42A82; 42C10; 43A35
DOI:10.3842/SIGMA.2016.103
DOI:10.3842/SIGMA.2016.103
Посилання:
Strictly Positive Definite Kernels on a Product of Spheres II / J.C. Guella, V.A. Menegatto, A.P. Peron // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 20 назв. — англ.
Підтримка:
The authors are grateful to the referees for their valuable comments and suggestions. Second
author acknowledges partial financial support from FAPESP, grant 2014/00277-5. Likewise, the
third author acknowledges support from the same foundation, under grants 2014/25796-5 and
2016/03015-7.
Дата:
2016
Переглядів:
532
Завантажень:
262
Анотація:
We present, among other things, a necessary and sufficient condition for the strict positive definiteness of an isotropic and positive definite kernel on the cartesian product of a circle and a higher dimensional sphere. The result complements similar results previously obtained for strict positive definiteness on a product of circles [Positivity, to appear, arXiv:1505.01169] and on a product of high dimensional spheres [J. Math. Anal. Appl. 435 (2016), 286-301, arXiv:1505.03695].
