Fourier Analysis on Groups.

By S. E. Puckette, W. Rudin. 1965

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Citations in the corpus

Adaptivity and Computation-Statistics Tradeoffs for Kernel and Distance based High Dimensional Two Sample Testing (2015, background): “For example, by Bochner’s theorem (see Rudin [1962]), the population quantity gMMD 2 is precisely (up to constants) x ] is the characteristic function of X at frequency t (similarly ϕ Y ( t ) ), and the population eED is precisely (up to constants) is the population CDF of X when projected along…”
Random Feature Maps for Dot Product Kernels (2012, background): “Their result, building upon a classical result in harmonic analysis called Bochner’s Theorem (refer to Rudin, 1962), shows how to, in some sense, embed the non-linear feature space (i.e.”
Kernel Continual Learning (2021, methodology): “Rahimi & Recht (2007) introduced an algorithm to approximate translation-invariant kernels using explicit feature maps, which is theoretically underpinned by Bochner’s theorem (Rudin, 1962).”
Shift Invariant Spaces on LCA Groups (2009, background): “For details and proofs see [14],[7], [8].”
Higher moments of convolutions (2011, background): “It is well– known [22] that the dual group Ĝ is isomorphic to G in the case.”
Random features for Kernel Deep Convex Network (2013, background): “Equation (1) can be approximated as: f (x) ≈ i∈S β i φ(x)φ(x i ) = i∈S β i k(x, x i ) (3) Although computation and storage are lower with a smaller set of training samples, this approach requires O(N L 2 ) computation cost to search a subset of size L sampled among N vectors.”
Generalized KYP lemma: unified frequency domain inequalities with design applications (2005, background): “However, using the ideas of [9], [10], [53], and [54], the problem can be made tractable when the specifications are given by inequality constraints on the gain only.”
A quantitative version of the idempotent theorem in harmonic analysis (2006, background): “Introduction Let us begin by stating the idempotent theorem.”
Some new inequalities in additive combinatorics (2012, background): “It is well– known [16] that the dual group Ĝ is isomorphic to G in the case.”
Random Features for Large-Scale Kernel Machines (2007, background): “The following classical theorem from harmonic analysis provides the key insight behind this transformation: Theorem 1 (Bochner [15]) .”
From Dependence to Causation (2016, unknown): “See Section 1.4.3 from (Rudin, 1962).”
Existence and Regularity of Weak Solutions to the Quasi-Geostrophic Equations in the Spaces Lp or $$\dot{H}^{-1/2}$$ (2007, background): “is non-negative is a consequence of the Bochner theorem (see [ 22 ]) and that x → e −|x|”
Uniform approximation of functions with random bases (2008, methodology): “We explored this result, which is based on Bochner’s theorem [21], in [4].”
Modulation Spaces on Locally Compact Abelian Groups (2003, background): “For further generalities concerning harmonic analysis see [29], [40], [38].”
Rigidity and non-recurrence along sequences (2011, background): “It follows that the set of denominators is the union of two lacunary sets and hence is a Sidon set ([28],[56]).”