Weyl transforms associated with the Heisenberg group

In this paper, we define the Wigner transform and the corresponding Weyl transform associated with the Heisenberg group. We established some harmonic analysis results. Then we present that the Weyl transform with the Sp-valued symbol in Lp (p∈[1,2]) is not only bounded but also compacted, while when 2<p<+∞, the Weyl transform is not a bounded operator.     

On spherical expansions of zonal functions on Euclidean spheres

This paper describes a new approach to the problem of computing spherical expansions of zonal functions on Euclidean spheres. We derive an explicit formula for the coefficients of the expansion expressing them in terms of the Taylor coefficients of the profile function rather than (as done usually) in terms of its integrals against Gegenbauer polynomials. Our proof of this result is based on a polynomial identity equivalent to the canonical decomposition of homogeneous polynomials and uses only basic properties of this decomposition together with simple facts concerning zonal harmonic polynomials. As corollaries, we obtain direct and apparently new derivations of the so-called plane wave expansion and of the expansion of the Poisson kernel for the unit ball. Received: 26 January 2007     

On the α-amenability of hypergroups

Let UC(K) denote the Banach space of all bounded uniformly continuous functions on a hypergroup K. The main results of this article concern the α-amenability of UC(K) and quotient and product of hypergroups. It is also shown that a Sturm-Liouville hypergroup with a positive index is α-amenable if and only if α = 1. Author’s address: Dietlinden Stra?e 16, 80802 München, Germany     

Permanents,Doty coalgebras and dominant dimension of Schur algebras

A (hidden) multiplication on _AZ(n,r)$A_{\mathbb{Z}}(n,r)$, the Z$\mathbb{Z}$-dual of the integral Schur algebra _SZ(n,r)$S_{\mathbb{Z}}(n,r)$ is explicitly constructed, possibly without a unit. The image of the multiplication map is shown to be spanned by bipermanents. Let k   be any field of characteristic p>0$p>0$. The image of the induced multiplication on _Ak(n,r)=_AZ(n,r)_⊗Zk$A_k(n,r)=A_{\mathbb{Z}}(n,r){\otimes }_{\mathbb{Z}}k$ turns out to coincide with the Doty coalgebra _Dn,r,p$D_{n,r,p}$ of truncated symmetric powers. Combined with a new straightening formula for bipermanents, it is proved that such a multiplication induces an isomorphism _Ak(n,r)_⊗Sk(n,r)Ak(n,r)≅_Ak(n,r)$A_k(n,r){\otimes }_{S_k(n,r)}{A}_k(n,r)\cong A_k(n,r)$ as _Sk(n,r)$S_k(n,r)$-bimodules if and only if r≤n(p−1)$r\le n(p-1)$, if and only if _Dn,r,p=_Ak(n,r)$D_{n,r,p}=A_k(n,r)$. As a result, _Sk(n,r)$S_k(n,r)$ is a gendo-symmetric algebra, and its dominant dimension is at least two and admits a combinatorial characterization as long as r≤n(p−1)$r\le n(p-1)$.     

On toric h-vectors of centrally symmetric polytopes

We prove tight lower bounds for the coefficients of the toric h-vector of an arbitrary centrally symmetric polytope generalizing previous results due to R. Stanley and the author using toric varieties. Our proof here is based on the theory of combinatorial intersection cohomology for normal fans of polytopes developed by G. Barthel, J.-P. Brasselet, K. Fieseler and L. Kaup, and independently by P. Bressler and V. Lunts. This theory is also valid for nonrational polytopes when there is no standard correspondence with toric varieties. In this way we can establish our bounds for centrally symmetric polytopes even without requiring them to be rational. Received: 24 March 2004     

Some spectral synthesis results by the analytic semigroup method

In 1980, J. Esterle proved the Wiener theorem forL ¹ (—) by a completely new method using analytic semigroup techniques. We show here how to extend the method in two different ways. First, it is shown that spectral synthesis for points on the real line is also provided by analytic semigroup techniques. Second, Esterle's proof may also be adapted to provide Wiener theorem for some elementary hypergroups. Eine überarbeitete Fassung ging am 24. 4. 2001 ein     

K+掺杂双钙钛矿Cs2AgInCl6的发光性质

采用固相球磨法制备了K^&#43;掺杂双钙钛矿Cs₂AgInCl₆纳米材料,该方法无需配体辅助,绿色环保。通过X射线衍射和拉曼光谱对晶体结构进行研究,通过激发光谱、发射光谱和时间分辨光谱对其发光性能进行研究。结果表明,Cs₂AgInCl₆为立方晶体,属于Fm3m空间群,由于宇称禁戒跃迁,其荧光量子产率(PLQY)低,小于0.1%。低于60%的K^&#43;掺杂主要取代Ag^&#43;的位置,引起Cs₂AgInCl₆的晶格膨胀,消除了晶格结构的反演对称性,打破了宇称禁戒跃迁,掺杂后Cs₂AgInCl₆的光致发光强度显著增强。K^&#43;的最佳掺杂比例为40%,Cs₂Ag_0.6K_0.4InCl₆材料发射中心波长为640 nm,半高宽为180 nm,平均荧光寿命达到29.2 ns,PLQY达到10.5%。当K^&#43;掺杂比例超过60%,K^&#43;开始取代Cs^&#43;的位置,产物发生相变,出现立方相的Cs_2-xK_1&#43;x-yAg_yInCl₆和单斜相的Cs_2-xK_1&#43;xInCl₆产物,这些产物由于强电子-声子耦合,非辐射复合占据主导地位。     

Cr3+掺杂Ca4HfGe3O12宽带近红外荧光粉的发光特性及应用

近红外荧光粉在生物活体成像领域展现出重要的应用前景。但活体成像用近红外荧光粉存在种类匮乏、耐温性差等瓶颈问题。采用固相法合成了宽带近红外Ca₄HfGe₃O₁₂∶ xCr^3&#43;(0≤x≤0.09)荧光粉。X射线衍射和能谱分析的结果表明Cr^3&#43;离子成功进入Ca₄HfGe₃O₁₂晶格。在469 nm蓝光激发下,Ca₄HfGe₃O₁₂∶xCr^3&#43;荧光粉发射出690~1 200 nm的宽带近红外光,峰值波长为825 nm (⁴T₂-⁴A₂),半高宽达到141 nm,Cr^3&#43;掺杂最佳浓度为0.03。依据激发光谱峰形和寿命衰减行为,证实Cr^3&#43;仅占据基质中一种阳离子格位。Ca₄HfGe₃O₁₂∶0.03Cr^3&#43;荧光粉的荧光量子效率为33.63%,该荧光粉发射光谱在400 K下的积分面积为室温下的60.5%,表明该样品具有优良的热稳定性。采用自制近红外荧光粉转换器件照射人手掌和滤波片遮挡的水果,观察到清晰地静脉血管和遮挡水果的轮廓。     

Some properties of horocycles on Damek-Ricci spaces

We prove that a Damek-Ricci space is symmetric if and only if the geodesic inversion preserves the set of horocycles.