Analysis of second order differential operators with complex coefficients on the Heisenberg group.
Analysis on Extended Heisenberg Group
In this paper we study Markov semigroups generated by Hörmander-Dunkl type operators on Heisenberg group.
Analysis on Lie groups.
Analysis on the Heisenberg Group and Estimates for Functions in Hardy Classes of Several Complex Variables.
Analytic continuation of representations and estimates of automorphic forms.
Analyticity for certain solutions of non-hypoelliptic differential operators on the Heisenberg group
Approximation of Hp-functions by Bochner-Riesz means of compact Lie groups.
Asymptotic behavior of solutions of Schrödinger inequalities on unbounded domains of nilpotent Lie groups
Asymptotic behavior of the invariant measure for a diffusion related to an NA group
On a Lie group NA that is a split extension of a nilpotent Lie group N by a one-parameter group of automorphisms A, the heat semigroup generated by a second order subelliptic left-invariant operator is considered. Under natural conditions there is a -invariant measure m on N, i.e. . Precise asymptotics of m at infinity is given for a large class of operators with Y₀,...,Yₘ generating the Lie algebra of S.
Asymptotic spherical analysis on the Heisenberg group
The asymptotics of spherical functions for large dimensions are related to spherical functions for Olshanski spherical pairs. In this paper we consider inductive limits of Gelfand pairs associated to the Heisenberg group. The group K = U(n) × U(p) acts multiplicity free on 𝓟(V), the space of polynomials on V = M(n,p;ℂ), the space of n × p complex matrices. The group K acts also on the Heisenberg group H = V × ℝ. By a result of Carcano, the pair (G,K) with G = K ⋉ H is a Gelfand pair. The main results...
Asymptotics of sums of subcoercive operators
We examine the asymptotic, or large-time, behaviour of the semigroup kernel associated with a finite sum of homogeneous subcoercive operators acting on a connected Lie group of polynomial growth. If the group is nilpotent we prove that the kernel is bounded by a convolution of two Gaussians whose orders correspond to the highest and lowest orders of the homogeneous subcoercive components of the generator. Moreover we establish precise asymptotic estimates on the difference of the kernel and the...