A German translation of Euler's articles on the polyhedron formula now available on the World Wide Web

The two articles on the polyhedron formula Euler published in his lifetime, Eneström 230 and 231, are now available on the World Wide Web in German translation.     

A characterization of normed spaces

We prove that the metric characterization of real normed spaces obtained by T. Oikhberg and H. Rosenthal can be obtained without a continuity assumption provided that the space is at least two-dimensional. In order to get this improvement we first need to understand the exceptional one-dimensional case.     

Group invariance and <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>-bounded operators

The Hilbert and Riesz transforms can be characterized up to scalar as the translation invariant operators that satisfy additionally certain relative invariance of conformal transformation groups. In this article, we initiate a systematic study of translation invariant operators from group theoretic viewpoints, and formalize a geometric condition that characterizes specific multiplier operators uniquely up to scalar by means of relative invariance of affine subgroups. After providing some interesting examples of multiplier operators having “large symmetry”, we classify which of these examples can be extended to continuous operators on L ^p (R ⁿ ) (1 < p < ∞). T. Kobayashi was partially supported by Grant-in-Aid for Scientific Research 18340037, Japan Society for the Promotion of Science. A. Nilsson was partially supported by Japan Society for the Promotion of Science.     

Banach空间上强混合的C_0-半群

证明了每个可分无限维复Banach空间上都存在一个强混合的C_0-半群,在加权函数空间上给出了转移半群是强混合的一个充要条件.     

Hypergroups and invariant complemented subspaces

Let K   be a hypergroup with a Haar measure. The purpose of the present paper is to initiate a systematic approach to the study of the class of invariant complemented subspaces of _L∞(K)$L_{\infty }(K)$ and _C0(K)$C_0(K)$, the class of left translation invariant w^?$w^{?}$-subalgebras of _L∞(K)$L_{\infty }(K)$ and finally the class of non-zero left translation invariant C^?$C^{?}$-subalgebras of _C0(K)$C_0(K)$ in the hypergroup context with the goal of finding some relations between these function spaces. Among other results, we construct two correspondences: one, between closed Weil subhypergroups and certain left translation invariant w^?$w^{?}$-subalgebras of _L∞(K)$L_{\infty }(K)$, and another, between compact subhypergroups and a specific subclass of the class of left translation invariant C^?$C^{?}$-subalgebras of _C0(K)$C_0(K)$. By the help of these two characterizations, we extract some results about invariant complemented subspaces of _L∞(K)$L_{\infty }(K)$ and _C0(K)$C_0(K)$.     

Collineation groups of translation planes admitting hyperbolic Buekenhout or parabolic Buekenhout-Metz unitals

It is shown that for every semifield spread in PG(3,q) and for every parabolic Buekenhout-Metz unital, there is a collineation group of the associated translation plane that acts transitively and regularly on the affine points of the parabolic unital. Conversely, any spread admitting such a group is shown to be a semifield spread. For hyperbolic Buekenhout unitals, various collineation groups of translation planes admitting such unitals and the associated planes are determined.     

On translations of complete first order theories

In this paper, some basic properties of automorphisms of first order languages and some examples are presented. In particular, an omitting types theorem is proved.     

Permissible growth rates for Birkhoff type universal harmonic functions

A harmonic function H on is said to be universal (in the sense of Birkhoff) if its set of translates is dense in the space of all harmonic functions on with the topology of local uniform convergence. The main theorem includes the result that such functions, H, can have any prescribed order and type. The growth result is compared with a similar known theorem for G.D. Birkhoff's universal holomorphic functions and contrasted with known growth theorems for MacLane-type universal harmonic and holomorphic functions.     

A simple proof of P. Carter's theorem

We give a simple proof of the following result of P. Carter: Given a twist homeomorphism of an annulus with at most one fixed point in the interior of the annulus, then there exists an essential simple closed curve inside this annulus meeting its image in at most the (possible) interior fixed point.