On Soluble Minimax Groups.
Commutators and generators II.
Analyticity Properties of Spin Systems
Analyticity Properties of Spin Systems
On the theory of subnormal subgroups.
A Property of the Lower Central Series of a Group.
Intersections of Primary Powers of a Group.
Scattering theory with singular potentials. I. The two-body problem
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...
Heat kernels and Riesz transforms on nilpotent Lie groups
We consider pure mth order subcoercive operators with complex coefficients acting on a connected nilpotent Lie group. We derive Gaussian bounds with the correct small time singularity and the optimal large time asymptotic behaviour on the heat kernel and all its derivatives, both right and left. Further we prove that the Riesz transforms of all orders are bounded on the Lp -spaces with p ∈ (1, ∞). Finally, for second-order operators with real coefficients we derive matching Gaussian lower bounds...
On positive Rockland operators
Let G be a homogeneous Lie group with a left Haar measure dg and L the action of G as left translations on . Further, let H = dL(C) denote a homogeneous operator associated with L. If H is positive and hypoelliptic on we prove that it is closed on each of the -spaces, p ∈ 〈 1,∞〉, and that it generates a semigroup S with a smooth kernel K which, with its derivatives, satisfies Gaussian bounds. The semigroup is holomorphic in the open right half-plane on all the -spaces, p ∈ [1,∞]. Further extensions...
Commutators and generators.
Derivations, dynamical systems, and spectral restrictions.
Positive C...-semigroups on C*-algebras.
L₁-uniqueness of degenerate elliptic operators
Let Ω be an open subset of with 0 ∈ Ω. Furthermore, let be a second-order partial differential operator with domain where the coefficients are real, and the coefficient matrix satisfies bounds 0 < C(x) ≤ c(|x|)I for all x ∈ Ω. If for some λ > 0 where then we establish that is L₁-unique, i.e. it has a unique L₁-extension which generates a continuous semigroup, if and only if it is Markov unique, i.e. it has a unique L₂-extension which generates a submarkovian semigroup. Moreover...
Extremal invariant states
Unbounded derivations of von Neumann algebras
A note on groups of finite rank
The Schur multiplier of a generalized Baumslag-Solitar group
On inert subgroups of a group
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