Topic
Distribution (differential geometry)
About: Distribution (differential geometry) is a research topic. Over the lifetime, 911 publications have been published within this topic receiving 10149 citations.
Papers published on a yearly basis
Papers
More filters
Posted Content•
TL;DR: In this article, the authors characterize the class of distributions on an homogeneous Lie group that can be extended via Poisson integration to a solvable one-dimensional extension of the group.
Abstract: In this paper, we characterize the class of distributions on an homogeneous Lie group $\fN$ that can be extended via Poisson integration to a solvable one-dimensional extension $\fS$ of $\fN$. To do so, we introducte the $s'$-convolution on $\fN$ and show that the set of distributions that are $s'$-convolvable with Poisson kernels is precisely the set of suitably weighted derivatives of $L^1$-functions. Moreover, we show that the $s'$-convolution of such a distribution with the Poisson kernel is harmonic and has the expected boundary behaviour. Finally, we show that such distributions satisfy some global weak-$L^1$ estimates.
3 citations
3 citations
17 Jun 2013
TL;DR: In this paper, a classification of solutions of the first and second Painleve quations corresponding to a special distribution of poles at infinity is considered, and the relation between this distribution and singularities of the two-dimensional complex monodromy data manifold used for the pa- rameterization of the solutions is analyzed.
Abstract: A classification of solutions of the first and second Painleve equations corresponding to a special distribution of poles at infinity is considered. The relation between this distribution and singularities of the two-dimensional complex monodromy data manifold used for the pa- rameterization of the solutions is analyzed. It turns out that solutions of the Painlevee quations have no poles in a certain critical sector of the complex plane if and only if their monodromy data lie in the singularity submanifold. Such solutions belong to the so-called class of "truncated" solutions (integrales tronquee) according to P. Boutroux's classification. It is shown that all known special solutions of the first and second Painleve equations belong to this class.
3 citations
07 Nov 2017
TL;DR: A way of constructing anisotropic distributions on the hyperbolic space whose covariance matrices are explicitly known is presented, which remains valid on every manifold homeomorphic to vector spaces.
Abstract: Most of the parametric families of distributions on manifold are constituted of radial distributions. The main reason is that quantifying the anisotropy of a distribution on a manifold is not as straightforward as in vector spaces and usually leads to numerical computations. Based on a simple definition of the covariance on manifolds, this paper presents a way of constructing anisotropic distributions on the hyperbolic space whose covariance matrices are explicitly known. The approach remains valid on every manifold homeomorphic to vector spaces.
3 citations