Lectures on Fourier integrals : with an author's supplement on monotonic functions, Stieltjes integrals, and harmonic analysis

By S. Bochner, Morris Tenenbaum, H. Pollard. 1959

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1. Kenji Fukumizu
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Citations in the corpus

• Characteristic Kernels and Infinitely Divisible Distributions (2014, background): “A desirable property for representing probability distributions P ∈ P(X ) in an RKHS H is that different probability distributions P,Q ∈ P(X ), P 6= Q map to different elements mP 6= mQ in the RKHS H, i.e., the kernel mean map P 7→ mP is injective.”
• Universal Kernels (2006, background): “Recall that Bochner (1959) proved that K is a kernel if and only if there is a unique finite Borel measure µ on Rd such that k at any x ∈ Rd has the form k(x) := Z Rd ei(x,y)dµ(y).”
• Differentiable Compositional Kernel Learning for Gaussian Processes (2018, methodology): “Bochner’s Theorem (Bochner, 1959) establishes a bijection between complex-valued stationary kernels and positive finite measures using Fourier transform, thus providing an approach to analyze stationary kernels in the spectral domain (Wilson & Adams, 2013; Kom Samo & Roberts, 2015).”