Laguerre polynomials, restriction principle, and holomorphic representations of SL(2, R)

被引：14

作者：

Davidson, M ^{[1
]}

Olafsson, G

Zhang, G

机构：

[1] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

[2] Chalmers Univ Technol, Dept Math, S-41296 Gothenburg, Sweden

来源：

ACTA APPLICANDAE MATHEMATICAE | 2002年 / 71卷 / 03期

基金：

美国国家科学基金会;

关键词：

Laguerre polynomials; representation theory; Lie groups; special functions; Segal-Bargman transform; restriction principle; SL(2; R);

D O I：

10.1023/A:1015283100541

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The restriction principle is used to implement a realization of the holomorphic representations of SL(2,R) on L-2 (R+,t(alpha) dt) by way of the standard upper half plane realization. The resulting unitary equivalence establishes a correspondence between functions that transform according to the character theta right arrow e(-i(2n+alpha+1)theta) under rotations and the Laguerre polynomials. The standard recursion relations amongst Laguerre polynomials are derived from the action of the Lie algebra.

引用

页码：261 / 277

页数：17