The Whittaker Plancherel theorem

被引：0

作者：

Wallach, Nolan R. ^{[1
]}

机构：

[1] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

来源：

JAPANESE JOURNAL OF MATHEMATICS | 2024年 / 19卷 / 01期

关键词：

tempered; representation; isotypic component; Schwartz space; Harish-Chandra Schwartz Space; Whittaker functional; Jacquet integral; Primary; 22030; Secondary; 22045; VECTORS;

D O I：

10.1007/s11537-023-2230-5

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The purpose of this article is to give an exposition of a proof of the distributional form of the Whittaker Plancherel Theorem. The proof is an application of Harish-Chandra's Plancherel Theorem for real reductive groups and its exposition can be used as an introduction to Harish-Chandra's Plancherel Theorem. The paper follows the basic method in the author's original approach in his second volume on real reductive groups. An error in the calculation of the Whittaker Transform of a Harish-Chandra wave packet is fixed using a result of Raphael Beuzart-Plessis.

引用

页码：1 / 65

页数：65

共 50 条

[31] The extension of the Gauss-Whittaker theorem.
Lichnerowicz, A
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1937, 205 : 25 - 27
[32] Different forms of Plancherel theorem for fractional quaternion Fourier transform
Wei, Deyun
Li, Yuanmin
OPTIK, 2013, 124 (24): : 6999 - 7002
[33] The generalisation of the Plancherel theorem in the case of fourier integrals on the commutative topologies
Krein, M
COMPTES RENDUS DE L ACADEMIE DES SCIENCES DE L URSS, 1941, 30 : 484 - 488
[34] Central limit theorem for random partitions under the Plancherel measure
Bogachev, L. V.
Su, Z. G.
DOKLADY MATHEMATICS, 2007, 75 (03) : 381 - 384
[35] Central limit theorem for random partitions under the Plancherel measure
L. V. Bogachev
Z. G. Su
Doklady Mathematics, 2007, 75 : 381 - 384
[36] Plancherel theorem and quaternion Fourier transform for square integrable functions
Cheng, Dong
Kou, Kit Ian
COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2019, 64 (02) : 223 - 242
[37] A Whittaker-Plancherel Inversion Formula for SL2(DOUBLE-STRUCK CAPITAL C)
Qi, Zhi
Yang, Chang
JOURNAL D ANALYSE MATHEMATIQUE, 2021, 145 (01): : 235 - 256
[38] GENERALIZATION OF THE WHITTAKER-KOTELINIKOV-SHANNON SAMPLING THEOREM
DRYANOV, DP
DOKLADI NA BOLGARSKATA AKADEMIYA NA NAUKITE, 1985, 38 (10): : 1319 - 1322
[39] Generalization of Titchmarsh's theorem for the modified Whittaker transform
Soltani, Fethi
Aledawish, Saliha
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2023, 34 (03) : 261 - 273
[40] Paley-Wiener theorem and the Plancherel formula for the generalized Laplace transform
Bouzaffour, Fethi
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2013, 24 (09) : 757 - 770

← 1 2 3 4 5 →