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

Positive definite spherical functions on Olshanskii domains

Authors:	Joachim Hilgert Karl-Hermann Neeb

Affiliation:	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 , a real form of , and the analytic subgroup of corresponding to . The symmetric space together with a -invariant partial order 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 ${mathcal{M}}^{+} := {Hxcolon Hxge H}$ of . 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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