Related papers: Closed and sigma-finite measures on the orthogonal…

Let $\nu$ be a self similar measure on $\mathbb{R}^d$, $d\geq 2$, and let $\pi$ be an orthogonal projection onto a $k$-dimensional subspace. We formulate a criterion on the action of the group generated by the orthogonal parts of the IFS on…

This paper locally classifies finite-dimensional Lie algebras of conformal and Killing vector fields on $\mathbb{R}^2$ relative to an arbitrary pseudo-Riemannian metric. Several results about their geometric properties are detailed, e.g.…

In the context of orthogonal polynomials in the plane we introduce the notion of a polynomially small (PS) perturbation of a measure. In such a case we establish relative asymptotic results for the two sequences of the associated…

We study the following problem: given an Einstein metric on a manifold, characterize and study all Einstein metrics which are pointwise projective to the given one. By definition, two metrics are said to be pointwise projectively related if…

The explicit Verlinde formula for the dimension of conformal blocks, attached to a marked projective curve $\Sigma$, a simple Lie algebra $\mathfrak{g}$ over $\mathbb{C}$ and integrable highest weight modules of a fixed central charge of…

In 1950 Maharam asked whether every disintegration of a $\sigma$-finite measure into $\sigma$-finite measures is necessarily uniformly $\sigma$-finite. Over the years under special conditions on the disintegration, the answer was shown to…

We prove a certain duality relation for orthogonal polynomials defined on a finite set. The result is used in a direct proof of the equivalence of two different ways of computing the correlation functions of a discrete orthogonal polynomial…

Tiling spaces are constructed using a metric in which two tilings of $\mathbb{R}^n$ are close if and only if, after a small translation, they agree on a large ball around the origin. We construct analogous spaces to study random…

We give criteria for boundedness of the associated Bergman-type projections on Lp-spaces on Cn with respect to generalized Gaussian weights exp(-|z|^2m). Complete characterization is obtained for 0<m<=1 and 2n/(2n-1)<m<2; partial results…

We introduce a kind of finite truncation of the hypergeometric series and provide its discretized integral representation. This is motivated by recent results of Maesaka-Seki-Watanabe and Hirose-Matsusaka-Seki on the identity between…

Our main interest in this paper is chiefly concerned with the conditions characterizing \textit{orthogonal and symplectic abstract differential geometries}. A detailed account about the sheaf-theoretic version of the \textit{symplectic…

This article describes recent applications of algebraic geometry to noncommutative algebra. These techniques have been particularly successful in describing graded algebras of small dimension.

The geometry of (2,1) supersymmetric sigma-models is reviewed and the conditions under which they have isometry symmetries are analysed. Certain potentials are constructed that play an important role in the gauging of such symmetries. The…

Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.

We prove a compactness theorem for metrics with Bounded Integral Curvature on a fixed closed surface $\Sigma$. As a corollary, we obtain a compactification of the space of Riemannian metrics with conical singularities, where an accumulation…

According to the von Neumann-Halperin and Lapidus theorems, in a Hilbert space the iterates of products or, respectively, of convex combinations of orthoprojections are strongly convergent. We extend these results to the iterates of convex…

We show that a conformal connection on a closed oriented surface $\Sigma$ of negative Euler characteristic preserves precisely one conformal structure and is furthermore uniquely determined by its unparametrised geodesics. As a corollary it…

We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…

We show that every ring isomorphism between the algebras of locally measurable operators for type II$_\infty$ von Neumann algebras is similar to a real $^*$-isomorphism. This together with previous results by the author and…

We give a survey of recent classification results for crossed product von Neumann algebras arising from measure preserving group actions on probability spaces. This includes II_1 factors with uncountable fundamental groups and the…