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A Note on the Derivatives of Isotropic Positive Definite Functions on the Hilbert Sphere
Symmetry, integrability and geometry: methods and applications, Tome 15 (2019) Cet article a éte moissonné depuis la source Math-Net.Ru

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In this note we give a recursive formula for the derivatives of isotropic positive definite functions on the Hilbert sphere. We then use it to prove a conjecture stated by Trübner and Ziegel, which says that for a positive definite function on the Hilbert sphere to be in $C^{2\ell}([0,\pi])$, it is necessary and sufficient for its $\infty$-Schoenberg sequence to satisfy $\sum\limits_{m=0}^{\infty}a_m m^{\ell}\infty$.
Keywords: positive definite, isotropic, Hilbert sphere, Schoenberg sequences. 
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     author = {Janin J\"ager},
     title = {A {Note} on the {Derivatives} of {Isotropic} {Positive} {Definite} {Functions} on the {Hilbert} {Sphere}},
     journal = {Symmetry, integrability and geometry: methods and applications},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a80/}
}
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Janin Jäger. A Note on the Derivatives of Isotropic Positive Definite Functions on the Hilbert Sphere. Symmetry, integrability and geometry: methods and applications, Tome 15 (2019). http://geodesic.mathdoc.fr/item/SIGMA_2019_15_a80/

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