J. Rosenberg, A quick proof of Harish-Chandra's Plancherel theorem for spherical functions on a semisimple Lie group. Proc. Amer. Math. Soc. 63 (1977), 143-149.  Home/Search Document Not in Database Summary Related Articles Check |
This paper is cited in the following contexts:
Harmonic analysis on semisimple symmetric spaces - .. - van den Ban.. (Correct)
....Nevertheless, one cannot then conclude from (i) that in fact JF f = f because JF f is not compactly supported in general. The presence of D is important, for example it annihilates all the discrete series in L (G=H; The proof of Theorem 10 is very much inspired by Rosenberg s proof (see [58] or [46, Ch. IV, x7] of the inversion formula for the spherical Fourier transform on G=K (in which case one can take D = 1) A key step in both proofs is the use of a shift argument , originally used by Helgason for the proof of the Paley Wiener theorem, where the integration in J (after use of ....
J. Rosenberg, A quick proof of Harish-Chandra's Plancherel theorem for spherical functions on a semisimple Lie group, Proc. Amer. Math. Soc. 63 (1977), 143-149.
Harmonic Analysis on Reductive Symmetric Spaces - van den Ban, Schlichtkrull (Correct)
....0 (x)Ff( c( 1 d : 6) Note that the usual Plancherel measure jc( j 2 d is hidden by the fact that Ff( equals 1=c( times the usual spherical Fourier transform f( the star denotes complex conjugation. A simpler proof of this formula was later given by J. Rosenberg, [46], based on a part of Helgason s proof of the Paley Wiener theorem (see [39] Ch. IV, 7) We will now discuss a part of this proof, since its generalization to G=H is used in the statement of the inversion formula. In Helgason s Paley Wiener argument, one exploits the Harish Chandra expansion ....
J. Rosenberg, A quick proof of Harish-Chandra's Plancherel theorem for spherical functions on a semisimple Lie group. Proc. Amer. Math. Soc. 63 (1977), 143-149.
The most-continuous part of the Plancherel.. - van den Ban.. (1995) (7 citations) (Correct)
....analysis, primarily due to Harish Chandra and Helgason ( 22] 23] 24] and [29] We shall see that L 2 mc (G=H) L 2 (G=H) in this case. Thus we retrieve in (2) the Plancherel decomposition of L 2 (G=H) A major simplification of the proof of this decomposition was found by Rosenberg [36], who used techniques inspired by Helgason s Paley Wiener theorem (see also [30] IV, x7) For the present generalization to arbitrary G=H we use ideas inspired by those of Rosenberg. In fact, we also obtain a Paley Wiener theorem for G=H (that is, we determine the Fourier image of the space C ....
J. Rosenberg, A quick proof of Harish-Chandra's Plancherel theorem for spherical functions on a semisimple Lie group. Proc. Amer. Math. Soc. 63 (1977), 143-149.
Harmonic analysis on semisimple symmetric spaces - .. - van den Ban.. (1997) (Correct)
....one cannot then conclude from (i) that in fact J F f = f because J F f is not compactly supported in general. The presence of D is important, for example it annihilates all the discrete series in L 2 (G=H; The proof of Theorem 10 is very much inspired by Rosenberg s proof (see [58] or [46, Ch. IV, x7] of the inversion formula for the spherical Fourier transform on G=K (in which case one can take D = 1) A key step in both proofs is the use of a shift argument , originally used by Helgason for the proof of the Paley Wiener theorem, where the integration in J (after use ....
J. Rosenberg, A quick proof of Harish-Chandra's Plancherel theorem for spherical functions on a semisimple Lie group, Proc. Amer. Math. Soc. 63 (1977), 143-149.
A Residue Calculus for Root Systems - Van Den Ban (2000) (1 citation) (Correct)
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J. Rosenberg, A quick proof of Harish-Chandra's Plancherel theorem for spherical functions on a semisimple Lie group. Proc. Amer. Math. Soc. 63 (1977), 143-149.
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