Displaying similar documents to “On the eigenvalue asymptotics of certain Schrödinger operators”

Asymptotics of sums of subcoercive operators

Nick Dungey, A. ter Elst, Derek Robinson (1999)

Colloquium Mathematicae

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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...

Some estimates concerning the Zeeman effect

Wiesław Cupała (1993)

Studia Mathematica

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The Itô integral calculus and analysis on nilpotent Lie grops are used to estimate the number of eigenvalues of the Schrödinger operator for a quantum system with a polynomial magnetic vector potential. An analogue of the Cwikel-Lieb-Rosenblum inequality is proved.

Nilpotent elements and solvable actions.

Mihai Sabac (1996)

Collectanea Mathematica

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In what follows we shall describe, in terms of some commutation properties, a method which gives nilpotent elements. Using this method we shall describe the irreducibility for Lie algebras which have Levi-Malçev decomposition property.

Square roots of perturbed subelliptic operators on Lie groups

Lashi Bandara, A. F. M. ter Elst, Alan McIntosh (2013)

Studia Mathematica

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We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators with complex bounded coefficients, which may have lower order terms. In this general setting we deduce inhomogeneous estimates. In case the group is nilpotent and the subelliptic operator is pure second order, we prove stronger homogeneous estimates. Furthermore, we prove Lipschitz stability of the estimates...