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We prove that the reproducing kernel Hilbert spaces (RKHS) of a deep neural tangent kernel and the Laplace kernel include the same set of functions, when both kernels are restricted to the sphere $\mathbb{S}^{d-1}$.
Positive definite functions on spheres
I. J. Schoenberg · 1942
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Theory of reproducing kernels
N. Aronszajn · 1950
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Laplace transforms
M. R. Spiegel · 1965
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Positive definite functions on spheres
N. H. Bingham · 1973
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Introduction to the theory and application of the Laplace transformation
G. Doetsch · 1974
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Mercer’s theorem, feature maps, and smoothing
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Y. Cho and L. K. Saul · 2009
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Spherical harmonics and approximations on the unit sphere: an introduction , volume 2044
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