Let W be a real symplectic space and(G,G')an irreducible dual pair in Sp(W),in the sense of Howe,with G compact.Let G be the preimage of G in the metaplectic group Sp(W).Given an irreducible unitary representation...Let W be a real symplectic space and(G,G')an irreducible dual pair in Sp(W),in the sense of Howe,with G compact.Let G be the preimage of G in the metaplectic group Sp(W).Given an irreducible unitary representation II of G that occurs in the restriction of the Weil representation to G,let On denote its character.We prove that,for a suitable embedding T of Sp(W)in the space of tempered distributions on W,the distribution T(On)admits an asymptotic limit,and the limit is a nilpotent orbital integral.As an application,we compute the wave front set of II',the representation of G dual to II,by elementary means.展开更多
In this note, we use the so-called microlocal energy method to give a characterization of the Gevrey-Sobolev wave front set WF<sub>(</sub>H<sub>T,σ</sub><sup>S</sup> （u）, which w...In this note, we use the so-called microlocal energy method to give a characterization of the Gevrey-Sobolev wave front set WF<sub>(</sub>H<sub>T,σ</sub><sup>S</sup> （u）, which will be useful in the study of non-linear microlocal analysis in Gevrey classes.展开更多
As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been invest...As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been investigated. By using the Level Set method, the transformation of a solitary wave over a front step was simulated. The results were in good agreement with laboratory experiments.展开更多
This paper deals with the Gevreg-hypoellipticity for a class of totally characteristic operators with the elliptic condition and the discrete boundary spectrum condition respectively.
基金the University of Oklahoma for hospitality and financial supporthospitality and financial support from the Université de Lorraine+1 种基金partial support from NSA (Grant No. H98230-13-1-0205)NSF (Grant No. DMS-2225892)
文摘Let W be a real symplectic space and(G,G')an irreducible dual pair in Sp(W),in the sense of Howe,with G compact.Let G be the preimage of G in the metaplectic group Sp(W).Given an irreducible unitary representation II of G that occurs in the restriction of the Weil representation to G,let On denote its character.We prove that,for a suitable embedding T of Sp(W)in the space of tempered distributions on W,the distribution T(On)admits an asymptotic limit,and the limit is a nilpotent orbital integral.As an application,we compute the wave front set of II',the representation of G dual to II,by elementary means.
基金Research supported by grants of the Natural Science Foundation of Chinathe State Education Committee and the Huacheng Foundation.
文摘In this note, we use the so-called microlocal energy method to give a characterization of the Gevrey-Sobolev wave front set WF<sub>(</sub>H<sub>T,σ</sub><sup>S</sup> （u）, which will be useful in the study of non-linear microlocal analysis in Gevrey classes.
文摘As a new method, the Level Set method had been developed to compute the interface of two-phase flow. The basic mathematical theory and the detailed method to solve the free surface hydrodynamic problem had been investigated. By using the Level Set method, the transformation of a solitary wave over a front step was simulated. The results were in good agreement with laboratory experiments.
基金Supported by National Natural Science Foundation of P.R.China
文摘This paper deals with the Gevreg-hypoellipticity for a class of totally characteristic operators with the elliptic condition and the discrete boundary spectrum condition respectively.
