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http://www.math.tau.ac.il/~bernstei/Publication_list/publication_texts/Ber-Plancherel-JGF.pdf
ON THE SUPPORT OF PLANCHEREL MEASURE 667 diverges for any d, i.e. the corresponding forms are not tempered. Thus, the analytic necessary condition shows that only representations with s E I IR (i.e. representations of the principle series) contribute to the spectral decomposition ofL 2(X). Example 2. G = SL(2, IR), F = SL(2, Z), X = C/I’. The space X has poly-
https://www.sciencedirect.com/science/article/pii/0393044088900241
ON THE SUPPORT OF PLANCHEREL MEASURE 685 Similarly, Q1 is supported in B2x, and for all y E B2x, Q1 (y) ~ Q3 (x). Thus f Q1 dm1 Q3(x) - mx(B2 - x) C Q3(x), and since the integral is comparable to d we get the second inequality, d ~ C2 Q3 (x).Cited by: 115
http://adsabs.harvard.edu/abs/1988JGP.....5..663B
Abstract Let G be a real reductive group. As follows from Plancherel formula for G, proved by Harish-Chandra, only tempered representations of G contribute to the decomposition of the regular representation in L 2 (G). We give a simple direct proof of this …
http://benjaminlharris.weebly.com/uploads/1/0/9/5/109534355/sphericity_1.19.pdf
Plancherel formula for X R involves parameters closely related to real forms of a X. IThe work of Delorme-Knop-Kr otz-Schlichtkrull determines the support of the Plancherel measure for a spherical variety up to the twisted discrete spectrum. This reduction involves parameters closely related to the split part of a real form of a X.
https://www.researchgate.net/publication/254897450_The_Central_Support_of_the_Plancherel_Measure_of_an_Affine_Hecke_Algebra
Oct 15, 2013 · The Central Support of the Plancherel Measure of an Affine Hecke Algebra Article (PDF Available) in Moscow Mathematical Journal 7(4) · October 2013 with 6 Reads How we measure 'reads'
https://digitalcommons.lsu.edu/gradschool_disstheses/7347/
But the third "more" invariant formula describes Plancherel measure on a support expressed in terms of rotations, dilations, and translations. Actually it is not canonical since it still depends on choices of bases for F3,2. Our goal is to redescribe Plancherel measure on a support expressed in terms of Aut*(g).Cited by: 1
https://www.math.ubc.ca/~cass/research/pdf/pl.pdf
On the Plancherel measure for the continuous spectrum of the modular group 2 • The function c(s) is smooth on RE (s) = 1/2. • For RE (s) = 1/2 it satisfies c(s) = 1, c(s)c(1−s) = 1 . The function Esalso satisfies the growth condition Es(z) = Es,0(y) +O(y−N) = ys+c(s)y1−s+O(y−N) for all …
https://en.wikipedia.org/wiki/Plancherel_theorem_for_spherical_functions
The Plancherel theorem gives the eigenfunction expansion of radial functions for the Laplacian operator on the associated symmetric space X; it also gives the direct integral decomposition into irreducible representations of the regular representation on L 2 ( X ).
https://arxiv.org/abs/math/9905032
Our approach is based on an exact determinantal formula for the correlation functions of the poissonized Plancherel measures involving a new kernel on the 1-dimensional lattice. This kernel is expressed in terms of Bessel functions and we obtain it as a degeneration of the hypergeometric kernel from the paper math.RT/9904010 by Borodin and Olshanski. Our asymptotic analysis relies on the classical …Cited by: 1
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