Exact power series in the asymptotic expansion of the matrix coefficients with the corner $K$-type of $P_J$-principal series representations of $Sp(2,R)$

Journal of Mathematical Sciences

IIDA, Masatoshi¹  ODA, Takayuki¹ 

关键词: Generalized functions;    ultradifferentiable functions;    Colombeau algebra;    wave front;    microlocal analysis;    Denjoy-Carleman classes;    Gevrey generalized functions;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Let$G$beasymplecticLiegroupofrank$2$,$Sp(2,mathbb{R})$and$P_J$beitsmaximalparabolicsubgroupcalledtheJacobiparabolicsubgroupwithnon-abelianunipotentradica.Theradialpartofmatrixcoefficientsofthe$P_J$-principalseriesrepresentationsof$G$werestudiedinrelationtotheAppell'shypergeometricfunction.Theleadingtermsoftheexpansionofthefunctionaroundtheinfinitywerewellinvestigatedingeneralcases(semisimpleLiegroupsandrepresentations).Inthispaper,wedeterminethepowerseriesexpansionotherthanleadingtermsfortheabovespecialcase.

【 授权许可】

Unknown