A real p-homogeneous seminorm with square property is submultiplicative

A real seminorm with square property is submultiplicative

A seminorm with square property on a real associative algebra is submultiplicative

通过格序代数中的子乘法格半范数实现序到环理想

Order-to-ring ideals via submultiplicative lattice seminorms in lattice-ordered algebras

本文刻画了具有序到环理想性质的格序代数，证明阿基米德格序代数具有该性质当且仅当它是f-代数且具有零半范数元素为幂零元的子乘法格半范数，并推广到半素f-代数的情形。

含单位元交换R-代数的截断矩问题

The Truncated Moment Problem for Unital Commutative R-Algebras

该研究针对含单位元交换实代数的截断矩问题，给出了配备次可乘半范数时线性泛函积分表示的存在准则，并推广至无拓扑情形，拓展了经典截断矩问题的相关结果。

Traces for homogeneous Sobolev spaces in infinite strip-like domains

In this paper we construct a trace operator for homogeneous Sobolev spaces defined on infinite strip-like domains. We identify an intrinsic seminorm on the resulting trace space that makes the trace operator bounded and allows us to construct a bounded right inverse. The intrinsic seminorm involves two features not encountered in the trace theory of bounded Lipschitz domains or half-spaces. First, due to the strip-like structure of the domain, the boundary splits into two infinite disconnected components. The traces onto each component are not completely independent, and the intrinsic seminorm…

Characterisation of homogeneous fractional Sobolev spaces

Our aim is to characterize the homogeneous fractional Sobolev-Slobodecki\uı spaces $\mathcal{D}^{s,p} (\mathbb{R}^n)$ and their embeddings, for $s \in (0,1]$ and $p\ge 1$. They are defined as the completion of the set of smooth and compactly supported test functions with respect to the Gagliardo-Slobodecki\uı seminorms. For $s\,p < n$ or $s = p = n = 1$ we show that $\mathcal{D}^{s,p}(\mathbb{R}^n)$ is isomorphic to a suitable function space, whereas for $s\,p \ge n$ it is isomorphic to a space of equivalence classes of functions, differing by an additive constant. As one of our main tools, we…

紧致情形下矩泛函的内蕴特征

An intrinsic characterization of moment functionals in the compact case

本文基于线性泛函内蕴的增长条件，给出了含幺交换实代数上具有紧致支撑的矩泛函的新特征，精确识别了表示 Radon 测度的紧致支撑，并推导出计算单点集测度的公式及支撑为有限集的充要条件。