Displaying similar documents to “The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms”

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.

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...

Malliavin calculus for stable processes on homogeneous groups

Piotr Graczyk (1991)

Studia Mathematica

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Let μ t t > 0 be a symmetric semigroup of stable measures on a homogeneous group, with smooth Lévy measure. Applying Malliavin calculus for jump processes we prove that the measures μ t have smooth densities.