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Differentiable Positive Definite Kernels on Spheres
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Published/Copyright:
June 9, 2010
Abstract
We analyze term-by-term differentiability of uniformly convergent series of the form 
, where Sm–1 is the unit sphere in 
, and {Yk} is a sequence of spherical harmonics or even more general functions. Since this class of kernels includes the continuous positive definite kernels on Sm–1, the results in this paper will show that, under certain conditions, the action of convenient differential operators on positive definite (strictly positive definite) kernels on Sm–1 generate positive definite kernels.
Received: 2007-07-02
Revised: 2008-09-15
Published Online: 2010-06-09
Published in Print: 2009-June
© Heldermann Verlag
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Articles in the same Issue
- Generalized Solutions to a Non Lipschitz-Cauchy Problem
- Bloch Varieties of Higher-Dimensional, Periodic Schrödinger Operators
- Specializing Aronszajn Trees and Preserving Some Weak Diamonds
- Variation of Constants Formula for Hyperbolic Systems
- Differentiable Positive Definite Kernels on Spheres
- When an Atomic and Complete Algebra of Sets is a Field of Sets with Nowhere Dense Boundary
- Directional Convex Extensions of the Convex Valued Maps
- On Whitney Convergence
