Results 21 to 30 of about 307 (54)
Averages and the $\ell^{q,1}$-cohomology of Heisenberg groups [PDF]
, 2019 Averages are invariants defined on the $\ell^1$ cohomology of Lie groups. We prove that they vanish for abelian and Heisenberg groups. This result completes work by other authors and allows to show that the $\ell^1$ cohomology vanishes in these ...
Pansu, Pierre, Tripaldi, Francesca
core +3 more sources
Lower bounds for operators on graded Lie groups [PDF]
, 2013 In this note we present a symbolic pseudo-differential calculus on graded nilpotent Lie groups and, as an application, a version of the sharp Garding inequality.
Fischer, Veronique, Ruzhansky, Michael
core +4 more sources
Isometry Lie algebras of indefinite homogeneous spaces of finite volume
Proceedings of the London Mathematical Society, Volume 119, Issue 4, Page 1115-1148, October 2019., 2019 Abstract Let g be a real finite‐dimensional Lie algebra equipped with a symmetric bilinear form ⟨·,·⟩. We assume that ⟨·,·⟩ is nil‐invariant. This means that every nilpotent operator in the smallest algebraic Lie subalgebra of endomorphisms containing the adjoint representation of g is an infinitesimal isometry for ⟨·,·⟩.
Oliver Baues +2 more
wiley +1 more source
Hausdorff measure of the singular set of quasiregular maps on Carnot groups
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 35, Page 2203-2220, 2003., 2003 Recently, the theory of quasiregular mappings on Carnot groups has been developed intensively. Let ν stand for the homogeneous dimension of a Carnot group and let m be the index of the last vector space of the corresponding Lie algebra. We prove that the (ν − m − 1)‐dimensional Hausdorff measure of the image of the branch set of a quasiregular mapping ...
Irina Markina
wiley +1 more source
Lipschitz extensions of maps between Heisenberg groups [PDF]
, 2015 Let $\H^n$ be the Heisenberg group of topological dimension $2n+1$. We prove that if $n$ is odd, the pair of metric spaces $(\H^n, \H^n)$ does not have the Lipschitz extension ...
Balogh, Zoltan, Lang, Urs, Pansu, Pierre
core +4 more sources
M\"{o}bius deconvolution on the hyperbolic plane with application to impedance density estimation [PDF]
, 2010 In this paper we consider a novel statistical inverse problem on the Poincar\'{e}, or Lobachevsky, upper (complex) half plane. Here the Riemannian structure is hyperbolic and a transitive group action comes from the space of $2\times2$ real matrices of ...
Huckemann, Stephan F. +3 more
core +1 more source
Smoothness of convolution products of orbital measures on rank one compact symmetric spaces
, 2015 We prove that all convolution products of pairs of continuous orbital measures in rank one, compact symmetric spaces are absolutely continuous and determine which convolution products are in $L^{2}$ (meaning, their density function is in $L^{2 ...
Hare, Kathryn, He, Jimmy
core +1 more source
Holomorphic harmonic analysis on complex reductive groups
, 2007 We define the holomorphic Fourier transform of holomorphic functions on complex reductive groups, prove some properties like the Fourier inversion formula, and give some applications.
An, Jinpeng, Qian, Min, Wang, Zhengdong
core +1 more source
Yamabe-type equations on Carnot groups
, 2016 This article is concerned with a class of elliptic equations on Carnot groups depending of one real positive parameter and involving a critical nonlinearity.
Bisci, Giovanni Molica +1 more
core +1 more source
Dunkl kernel associated with dihedral group
, 2015 In this paper, we pursue the investigations started in \cite{Mas-You} where the authors provide a construction of the Dunkl intertwining operator for a large subset of the set of regular multiplicity values. More precisely, we make concrete the action of
Deleaval, Luc +2 more
core +3 more sources