A course in abstract harmonic analysis

By G. Folland. 1995

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Citations in the corpus

Steerable CNNs (2016, background): “This happens through a natural and important construction known as the induced representation (Mackey, 1952; 1953; 1968; Serre, 1977; Taylor, 1986; Folland, 1995; Kaniuth & Taylor, 2013).”
Spherical CNNs (2018, methodology): “This transform ﬁnds it roots in the representation theory of groups, but due to space constraints we will not go into details here and instead refer the interested reader to Sugiura (1990) and Folland (1995).”
A General Theory of Equivariant CNNs on Homogeneous Spaces (2018, methodology): “Here we restrict our attention to locally compact topological groups, for which we can define a well-behaved integral, which is used to define the convolution [Folland, 1995].”
Banach Gelfand Triples for Gabor Analysis (2008, unknown): “τ ∈ C with |τ | = 1 one can augment the phase space R× R̂d to the so-called Heisenberg group R× R̂d× T and the mapping (x, ω, τ) 7→ τMωTx defines a (true) unitary representation of the Heisenberg group [23], the so-called Schrödinger representation.”
Crossed products of C*-algebras (2007, methodology): “However, once we fix a measure /x, we could, as in [56] and [29], work with measurable sections of Borel Hilbert bundles.”
Quantization on Nilpotent Lie Groups (2016, methodology): “Our presentation there follows essentially the arguments of Folland and Stein [FS82].”
Foundations of Signal Processing (2014, methodology): “Finally, the text by Folland [30] has been written from a physicist’s point of view and offers an excellent treatment of partial differential equations.”
Scale-Equivariant Steerable Networks (2019, background): “Here μ(g′) is the Haar measure also known as invariant measure Folland (2016). For T ∼= R we have dμ(g′) = dg′.”
Stabilizers of Ergodic Actions of Lattices and Commensurators (2013, background): “Note that L(2)(G/H, ρH) gives a measurable field of Hilbert spaces where a measurable sequence of vector fields is given by ζn(H) = 1OnH where {On} is a countable basis for the topology of G (see Folland [Fol94] Section 7.”
Convolutional Networks for Spherical Signals (2017, background): “This transform ﬁnds it roots in the representation theory of groups, but due to space contraints we will not go into details here and instead refer to interested reader to Sugiura (1990); Folland (1995).”
Continuous Gabor transform for a class of non-Abelian groups (2012, background): “See [6], for a discussion of this topology on Ĝ.”
An overview of periodic elliptic operators (2015, background): “[55,75,113,220,239,245]), since in our situations this is usually not required.”
Reproducing formulas for generalized translation invariant systems on locally compact abelian groups (2014, background): “For more information on harmonic analysis on locally compact abelian groups, we refer the reader to the classical books [17, 31, 32, 44].”
Intertwiners between Induced Representations (with Applications to the Theory of Equivariant Neural Networks) (2018, methodology): “Such measures always exist for locally compact groups, thus covering most cases of interest [Folland, 1995].”