Harmonic analysis on symmetric spaces as complex analysis

被引：1

作者：

Gindikin, Simon ^{[1
]}

机构：

[1] Rutgers State Univ, Dept Math, Hill Ctr, Piscataway, NJ 08854 USA

来源：

AUTOMORPHIC FORMS AND RELATED GEOMETRY: ASSESSING THE LEGACY OF I.I. PIATETSKI-SHAPIRO | 2014年 / 614卷

关键词：

Cauchy-Fantappie integral formula; symmetric space; horosphere; horospherical transform; complex crown; Penrose transform; residue-class; TRANSFORM; SERIES;

D O I：

10.1090/conm/614/12249

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We discuss some results on complex analysis on semisimple Lie groups and more generally on complex symmetric spaces and their applications to the theory of representations. The focus is in the conception of Cauchy integral formula on symmetric spaces. The principal direction of applications is Gelfand's method of horospheres and an observation that we often need its complex versions for the harmonic analysis on real symmetric spaces.

引用

页码：69 / 80

页数：12

共 50 条

[1] Harmonic analysis on reductive symmetric spaces
van den Ban, E
Schlichtkrull, H
[J]. EUROPEAN CONGRESS OF MATHEMATICS, VOL I, 2001, 201 : 565 - 582
[2] HARMONIC-ANALYSIS ON NILPOTENT SYMMETRIC-SPACES
BENOIST, Y
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1983, 296 (12): : 489 - 492
[3] Harmonic Analysis on Quantum Complex Hyperbolic Spaces
Bershtein, Olga
Kolisnyk, Yevgen
[J]. SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS, 2011, 7
[4] Harmonic analysis for spinor fields in complex hyperbolic spaces
Camporesi, R
[J]. ADVANCES IN MATHEMATICS, 2000, 154 (02) : 367 - 442
[5] Harmonic analysis for differential forms on complex hyperbolic spaces
Pedon, E
[J]. JOURNAL OF GEOMETRY AND PHYSICS, 1999, 32 (02) : 102 - 130
[6] Harmonic analysis on symmetric Stein manifolds from the point of view of complex analysis
Gindikin, Simon
[J]. JAPANESE JOURNAL OF MATHEMATICS, 2006, 1 (01): : 87 - 105
[7] Harmonic analysis on symmetric Stein manifolds from the point of view of complex analysis
Simon Gindikin
[J]. Japanese Journal of Mathematics, 2006, 1 : 87 - 105
[8] Harmonic analysis of mean periodic functions on symmetric spaces and the Heisenberg group
Applebaum, Dave
[J]. MATHEMATICAL GAZETTE, 2011, 95 (534): : 571 - 572
[9] HARMONIC-ANALYSIS ON SEMISIMPLE SYMMETRIC-SPACES - A METHOD OF DUALITY
FLENSTEDJENSEN, M
[J]. LECTURE NOTES IN MATHEMATICS, 1984, 1077 : 166 - 209
[10] Lie Theory Harmonic Analysis on Symmetric Spaces - General Plancherel Theorems
Beltita, Daniel
[J]. REVUE ROUMAINE DE MATHEMATIQUES PURES ET APPLIQUEES, 2007, 52 (05): : 595 - 596

← 1 2 3 4 5 →