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     

一般有界区域上次线性椭圆方程改进的正解估计

在一般有界区域上，建立了次线性椭圆方程广义Ｄｉｒｉｃｈｌｅｔ问题改进的正解估计和有界强解的存在性定理．     

Reconstruction of Hp -Functions: Best Approximation,Regularization and Optimal Error Estimates

Let U be the open unit disc of the complex plane. We explicitly construct the best pointwise approximation for determining a function in the Hardy space H ^p (U) from measured data at a countable set of points in U whenever the data is exact. A regularization scheme is given to deal with the case of nonexact data. Moreover, optimal error estimates are also studied.     

Fixed point theorems in homotopically trivial spaces

We introduce a new concept of generalized Knaster–Kuratowski–Mazurkiewicz (KKM) family of sets and related to this we obtain fixed point theorems and sections results in homotopically trivial spaces.     

Asymptotics for eigenelements of Laplacian in domain with oscillating boundary: multiple eigenvalues

We study the asymptotic behavior of the solutions of a spectral problem for the Laplacian in a domain with rapidly oscillating boundary. We consider the case where the eigenvalue of the limit problem is multiple. We construct the leading terms of the asymptotic expansions for the eigenelements and verify the asymptotics.     

Extension of bounded holomorphic functions¶in convex domains

The E. Amar and G. Henkin theorem on the bounded extendability of bounded holomorphic functions from certain closed complex submanifolds of strictly pseudoconvex domains to the whole domain is generalized to the case of finite type convex domains and their intersections with affine linear hyperplanes. Suitable integral operators of Berndtsson–Andersson type are constructed and estimated for this purpose. Received: 7 July 2000     

Nombres de Tamagawa des groupes réductifs quasi-connexes

We define Tamagawa numbers for quasi-connected linear algebraic groups. This category of non-connected linear algebraic groups occurs naturally in the stabilization of the Arthur-Selberg trace formula. An expression for their Tamagawa numbers, needed for the stabilization process, is given in term of cohomological invariants generalizing results of Ono, Sansuc, Kottwitz and Kottwitz & Shestad. Received: 7 March 2000     

Spin Groups Over a Commutative Ring and the Associated Root Data

 Usual constructions of spin and Clifford groups, restricted to the case where the basic quadratic spaces is hyperbolic, are examined as those of group schemes over a commutative ring. Not surprisingly they yield indeed smooth and reductive group schemes, but the proof involves a lot of calculation and uses a connection with Jordan pairs. Maximal tori and their associated root data are also constructed explicitly. Received November 6, 2001; in revised form September 5, 2002 Published online May 9, 2003