Noncommutative Harmonic Analysis

By Michael Taylor. 1986

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Citations in the corpus

Spherical CNNs (2018, background): “Generalized Fourier analysis, sometimes called abstract- or noncommutative harmonic analysis, has a long history in mathematics and many books have been written on the subject (Sugiura, 1990; Taylor, 1986; Folland, 1995).”
Global quantization of pseudo-differential operators on compact Lie groups, SU(2), 3-sphere, and homogeneous spaces (2008, background): “However, the approach developed in this paper is different from that of [28, 29] since it relies on the group structure directly and thus we do not need to work in neighbourhoods of the neutral element and can approach global symbol classes directly.”
Pluri-potential theory on Grauert tubes of real analytic Riemannian manifolds, I (2011, methodology): “This formula is proved in [T] using the Poisson integral formula for a ball.”
Vector Diffusion Maps and the Connection Laplacian (2011, background): “All results and proofs in this section can be found in [15] and [38].”
The Atiyah-Singer index formula for subelliptic operators on contact manifolds. Part I (2008, background): “We recall some basic facts (see, for example, [Ta], [CG]).”
Hardy's inequality for fractional powers of the sublaplacian on the Heisenberg group (2015, background): “Taylor [29], and the monograph [10] of C.”
An extension problem for the CR fractional Laplacian (2013, background): “, Fontana and Morpurgo [8] that underlined the importance and nice PDE properties of these operators. There is a rich theory of pseudodiﬀerential operators on the Heisenberg group (see, for instance, [62]). In particular, the fractional sub-Laplacian is the inﬁnitesimal generators of a Levy process ”
A spectral multiplier theorem for a sublaplacian on SU(2) (2001, unknown): “, [35] or [38] for more details.”
The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups (2008, background): “xλ dλ 2π , where the equality is intended in the L2 sense. It has been known from more than 50 years that the Fourier transform generalizes to a wide class of locally compact groups (see for instance [14,19,25,26,32,45]). Next we brieﬂy present this generalization for groups satisfying the following”
Quantization on Nilpotent Lie Groups (2016, background): “Elements of the harmonic analysis on different groups can be also found in Taylor’s book [Tay86].”