Let X be a Riemannian symmetric space of non-compact type. We prove a theorem of holomorphic extension for eigenfunctions of the Laplace-Beltrami operator on X, by techniques from the theory of partial differential equations.

2008-12-03math.RT

The Bochner measure and holomorphic extension of elementary spherical functions

In this paper we determine the Bochner measure for spherical functions on a semi-simple Lie group of rank one.

2009-02-26math.RT

冠域边界处$K$-有限向量轨道映射的全纯延拓的多项式增长性

Polynomial growth of holomorphic extensions of orbit maps of $K$-finite vectors at the boundary of the crown

本研究将Krötz-Stanton延拓定理推广到任意连通半单李群，证明了$K$-有限向量轨道映射全纯延拓在冠域边界的多项式增长性，且其边值存在于分布向量空间中。

2025-01-16math.RT

Holomorphic horospherical duality "sphere-cone"

We describe a construction of complex geometrical analysis which corresponds to the classical theory of spherical harmonics.

2005-01-02math.CVmath.RT

The complex crown for homogeneous harmonic spaces

A theory of holomorphic extension of eigenfunctions on homogeneous harmonic spaces is developed.

2010-04-23math.RT

Holomorphic extension of representations: (I) automorphic functions

Let G be a connected, real, semisimple Lie group contained in its complexification G_C, and let K be a maximal compact subgroup of G. We construct a K_C-G double coset domain in G_C, and we show that the action of G on the K-finite vectors of any irreducible unitary representation of G has a holomorphic extension to this domain. For the resultant holomorphic extension of K-finite matrix coefficients we obtain estimates of the singularities at the boundary, as well as majorant/minorant estimates along the boundary. We obtain L^\infty bounds on holomorphically extended automorphic functions on G…

2006-01-10math.NTmath.RT

更多相关论文收起更多论文

The inversion formula and holomorphic extension of the minimal representation of the conformal group

The minimal representation $π$ of the indefinite orthogonal group $O(m+1,2)$ is realized on the Hilbert space of square integrable functions on $\mathbb R^m$ with respect to the measure $|x|^{-1} dx_1... dx_m$. This article gives an explicit integral formula for the holomorphic extension of $π$ to a holomorphic semigroup of $O(m+3, \mathbb C)$ by means of the Bessel function. Taking its `boundary value', we also find the integral kernel of the `inversion operator' corresponding to the inversion element on the Minkowski space $\mathbb R^{m,1}$.

2006-06-30math.FAmath.RT

Holomorphic extensions of eigenfunctions on $NA$ groups

Let $ X = G/K $ be a rank one Riemannian symmetric space of noncompact type. In view of the Iwasawa decomposition $ G = NAK $ of the underlying semisimple Lie group, we can also view $ X $ as the solvable extension $ S = NA $ of the Iwasawa group $ N$ which is known to be a $H$-type group. In this work we study the holomorphic extendability of eigenfunctions of the Laplace-Beltrami operator $ Δ_S$ on $ S $ to certain domains in the complexification of the nilpotent group $ N$. We can also do the same for any $H$-type group $ N $ not necessarily an Iwasawa group. The results are accomplished by…

2020-05-20math.CAmath.RT

单参数算子群的全纯扩张

Holomorphic extension of one-parameter operator groups

本文研究局部凸空间上单参数算子群的全纯扩张，并将其应用于 Lie 群酉表示的分布向量空间，为代数量子场论中标准子空间网的构造提供了新工具，同时揭示了方法在解析向量空间中的失效及相关的极大性结果。

2023-09-18math.FAmath.RT