Strictly positive definite functions on spheres
Lu, Tianshi
Lu, Tianshi
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2025-03
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Completely monotonic function,Positive definite function,Truncated power function
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Tianshi Lu, Strictly positive definite functions on spheres, Journal of Approximation Theory, Volume 306, 2025, 106120, ISSN 0021-9045, https://doi.org/10.1016/j.jat.2024.106120.
Abstract
In this paper, we proved that a positive definite radial function on Rd with support in [0,π] is strictly positive definite on the sphere Sd and real projective space RPd for odd d≥3. We also proved that the truncated power function (t−⋅)+(d+1)/2 is strictly positive definite on Sd and RPd for d≥2 and t∈(0,π]. © 2024 Elsevier Inc.
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Academic Press Inc.
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Journal of Approximation Theory
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00219045