The main thread through the paper is a careful analysis of the matrix coefficients for the discrete series and principal series of representations of [bold]SL (2, [bold]R). The paper is long, very technical and is not for the faint-hearted.
( Better - than - uniform Runge theorem ) Suppose that N * \ F is connected and locally connected . ... Armitage and Goldstein ( AG ) used fusion lemmas to prove Theorem 1 when ε is a positive multiple of the Green function with fixed ...
Harmonic Analysis on Symmetric Spaces – General Plancherel Theorems Jean-Philippe Anker, Bent Orsted ... The principal series for a reductive symmetric space II. ... W. Barker, Lp-harmonic analysis on SL(2, R), Mem. Amer. Math. Soc.
Re (A) = 1/2 , J. maps H'(R) to L*(R) (this is like an inequality due to Hardy: for f in H*(R) * dy to M'-- ) , I, l and ... of SL(2, R) by remarking that, if 0 < Re(A) < 1 , then "A acts uniformly boundedly on the completion of LP(R) ...
where my(X) f := (iff([Xs, ml, o] + trChy (l)))f, 2 y,(X) f := (20x0)–: IXr ml, m, 1994 ashx(), ml, ... of the principal series representation P" of the Lie group G9 = SL(2, C) to its real non-compact form SL(2, R) for p = -2, 6 = v-1.
L”-HARMONIC ANALYSIS ON SOME SIMPLE GROUPS In this section, we investigate the role played by the analytic families of ... discovered by R.A. Kunze and E.M. Stein [KS1] for SL(2,R) and (after various generalisations based on uniformly ...
2. Let B.G/ denote the Fourier-Stieltjes algebra of G: the space of all matrix coefficients of G, which turns out to be a ... SL.2;R// for p 2 .2;1/ are in fact abstractly isomorphic, as one can see by combining Wiersma's analysis [36] ...
... and consider T = l o(g")To(g) dg, (+) where dg is the unit Haar measure on G. (a) Show that Tintertwines the ... If f e S-1+** and h e S-1-##, show that 27t (f, h) = f(cos 6, sin 6) h(cos 6, sin 6) du 0 gives a pairing between ST" ...
( SN ( G ) designates the Nth partial sum of the Fourier series of G. ) To prove the uniform convergence on R , we compute ( using Exercise 1.51 and Hölder's Inequality ) \ r ( ) -1 [ f ( nT ) ... Sampling and the Nyquist Rate a .
Our proof makes use of the transitivity of the action of Sp(2n,R) on the Lagrangian Grassmannian Lag(2n,R). Theorem 60. For every S ∈ Sp(2n,R) there exist two ... for given l, choose l transversal to both lP and Sl: l∩lP=l∩Sl={0}.