and operator algebras.
Haar measure and continuous representations of locally compact abelian groups
Let (X) be the algebra of all bounded operators on a Banach space X, and let θ: G → (X) be a strongly continuous representation of a locally compact and second countable abelian group G on X. Set σ¹(θ(g)): = λ/|λ| | λ ∈ σ(θ(g)), where σ(θ(g)) is the spectrum of θ(g), and let be the set of all g ∈ G such that σ¹(θ(g)) does not contain any regular polygon of (by a regular polygon we mean the image under a rotation of a closed subgroup of the unit circle different from 1). We prove that θ is uniformly...
Haar measure on linear groups over local skew fields.
Halbeinfache Automorphismengruppen von vierdimensionalen stabilen Ebenen sind quasi-einfach.
Hardy spaces and analytic continuation of Bergman spaces
Hardy spaces on affine symmetric spaces.
Hardy spaces on SU(2)
Hardy spaces on two-sheeted covering semigroups.
Hardy-Littlewood theory on unimodular groups
Hardy's inequality for compact Lie groups.
Hardy's theorem for the helgason Fourier transform on noncompact rank one symmetric spaces
Let G be a semisimple Lie group with Iwasawa decomposition G = KAN. Let X = G/K be the associated symmetric space and assume that X is of rank one. Let M be the centraliser of A in K and consider an orthonormal basis of L²(K/M) consisting of K-finite functions of type δ on K/M. For a function f on X let f̃(λ,b), λ ∈ ℂ, be the Helgason Fourier transform. Let be the heat kernel associated to the Laplace-Beltrami operator and let be the Kostant polynomials. We establish the following version...
Hardy-type inequalities related to degenerate elliptic differential operators
We prove some Hardy-type inequalities related to quasilinear second-order degenerate elliptic differential operators . If is a positive weight such that , then the Hardy-type inequalityholds. We find an explicit value of the constant involved, which, in most cases, results optimal. As particular case we derive Hardy inequalities for subelliptic operators on Carnot Groups.
Harmonic analysis and unitary group representations : the development from 1927 to 1950
Harmonic analysis for spinors on real hyperbolic spaces
We develop the L² harmonic analysis for (Dirac) spinors on the real hyperbolic space Hⁿ(ℝ) and give the analogue of the classical notions and results known for functions and differential forms: we investigate the Poisson transform, spherical function theory, spherical Fourier transform and Fourier transform. Very explicit expressions and statements are obtained by reduction to Jacobi analysis on L²(ℝ). As applications, we describe the exact spectrum of the Dirac operator, study the Abel transform...
Harmonic analysis in one-parameter metabelian nilmanifolds.
Harmonic analysis in weighted -spaces
Harmonic analysis of Abelian inner automorphism groups of von Neumann algebras.
Harmonic analysis on .
Harmonic analysis on semisimple -adic Lie algebras.
Harmonic functions on homogeneous spaces of commutator induced extensions of compact groups