Related papers: An orthogonality relation in complex normed spaces…

For the double complex structure of grading-restricted vertex algebra cohomology defined in \cite{Huang}, we introduce a multiplication of elements of double complex spaces. We show that the orthogonality and bi-grading conditions applied…

Let $(X,d)$ be a compact metric space. We consider the behavior of probability measures $\mu$ with the property that $$ \int_{X} d(x, y) d\mu(y) \qquad \mbox{is independent of}~x \in X.$$ It appears that such measures, when they exist,…

We prove necessary and sufficient integral conditions involving extremal distance for a conformal mapping of the unit disk to belong to the Hardy or weighted Bergman spaces. We also give characterizations for the Hardy number and the…

A (bar-and-joint) framework is a set of points in a normed space with a set of fixed distance constraints between them. Determining whether a framework is locally rigid - i.e. whether every other suitably close framework with the same…

We introduce a remarkable new family of norms on the space of $n \times n$ complex matrices. These norms arise from the combinatorial properties of symmetric functions, and their construction and validation involve probability theory,…

An orthogonality space is a set equipped with a symmetric and irreflexive binary relation. We consider orthogonality spaces with the additional property that any collection of mutually orthogonal elements gives rise to the structure of a…

Every diagonalmatrix D yields an endomorphism on the n-dimensional complex vectorspace. If one provides this space with Hoelder norms, we can compute the operator norm of D. We define homogeneous weighted spaces as a generalization of…

The space of $G$-invariant metrics on a homogeneous space $G/H$ is in one-to-one correspondence with the set of inner products on the tangent space $\fr{m}\cong T_{{\it o}}(G/H)$, which are invariant under the isotropy representation. When…

Discrete conjugate systems are quadrilateral nets with all planar faces. Discrete orthogonal systems are defined by the additional property of all faces being concircular. Their geometric properties allow one to consider them as proper…

Coarse geometry studies metric spaces on the large scale. Our goal here is to study dynamics from a coarse point of view. To this end we introduce a coarse version of topological entropy, suitable for unbounded metric spaces, consistent…

Fix a point in a finite-dimensional complex vector space and consider the sequence of iterates of this point under the composition of a unitary map with the orthogonal projection on the hyperplane orthogonal to the starting point. We prove…

We consider integrable systems that are connected with orthogonal separation of variables in complex Riemannian spaces of constant curvature. An isomorphism with the hyperbolic Gaudin magnet, previously pointed out by one of us, extends to…

Let $m,n\ge 2$ be integers. Denote by $M_n$ the set of $n\times n$ complex matrices. Let $\|\cdot\|_{(p,k)}$ be the $(p,k)$ norm on $M_{mn}$ with $1\leq k\leq mn$ and $2<p<\infty$. We show that a linear map $\phi:M_{mn}\rightarrow M_{mn}$…

A set of necessary and sufficient conditions under which an isotone mapping from a subset of a poset X to a poset Y has an extension to an isotone mapping from X to Y are found.

The purpose of this paper is to study the (different) notions of homo-derivations. These are additive mappings $f$ of a ring $R$ that also fulfill the identity \[ f(xy)=f(x)y+xf(y)+f(x)f(y) \qquad \left(x, y\in R\right), \] or (in case of…

We study embeddings of uniform Roe algebras which have "large range" in their codomain and the relation of those with coarse quotients between metric spaces. Among other results, we show that if $Y$ has property A and there is an embedding…

The problem of testing hypothesis that a density function has no more than $\mu$ derivatives versus it has more than $\mu$ derivatives is considered. For a solution, the $L^2$ norms of wavelet orthogonal projections on some orthogonal…

Let $X_0, X_1, ..., X_k$ with $k \in \IN\cup\{\infty\}$ be sequence spaces $($finite or infinite dimensional$)$ over $\IC$ or $\IR$ with absolute norms $N_i$ for $i = 0, ..., k$, $($i.e., with 1-unconditional bases$)$ such that $\dim X_0 =…

For a given compact Hausdorff space $X$, we construct the space $OS_{f}(X)$ of normed, order-preserving, weakly additive, positively homogeneous and semi-additive functionals (for brevity, semi-additive functionals) and it is proved that…

Let $\mathcal{M}$ be a von Neumann algebra with a normal semifinite faithful trace $\tau$. We prove that every continuous $m$-homogeneous polynomial $P$ from $L^p(\mathcal{M},\tau)$, with $0<p<\infty$, into each topological linear space $X$…