Positive definite spherical functions on Ol<IMG ALIGN=TOP HEIGHT=8 WIDTH=4>shanskii domains期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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Positive definite spherical functions on Olshanskii domains

Authors:	Joachim Hilgert Karl-Hermann Neeb

Institution:	Mathematisches Institut, Technische Universität Clausthal, Erzstr. 1, 38678 Clausthal-Zellerfeld, Germany ; Mathematisches Institut, Universität Erlangen, Bismarckstr. 1 1/2, 91054 Erlangen, Germany

Abstract:	Let be a simply connected complex Lie group with Lie algebra $\mathfrak{g}$ , $\mathfrak{h}$ a real form of $\mathfrak{g}$ , and the analytic subgroup of corresponding to $\mathfrak{h}$ . The symmetric space ${\mathcal{M}}=H\backslash G$ together with a -invariant partial order $\le$ is referred to as an Olshanskii space. In a previous paper we constructed a family of integral spherical functions $\phi _{\mu }$ on the positive domain ${\mathcal{M}}^{+} := \{Hx\colon Hx\ge H\}$ of ${\mathcal{M}}$ . In this paper we determine all of those spherical functions on ${\mathcal{M}}^{+}$ which are positive definite in a certain sense.

Keywords:	Positive definite function ordered symmetric space holomorphic representation spherical function involutive semigroup

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