The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms
The theory of Markov processes and the analysis on Lie groups are used to study the eigenvalue asymptotics of Dirichlet forms perturbed by scalar potentials.
On the eigenvalue asymptotics of certain Schrödinger operators
Subelliptic estimates on nilpotent Lie groups and the Cwikel-Lieb-Rosenblum inequality are used to estimate the number of eigenvalues for Schrödinger operators with polynomial potentials.
The Dirichlet boundary value problem for certain Schrödinger equations with magnetic vector potentials
The probabilistic approach to the Dirichlet boundary value problem for certain Schrödinger equations with magnetic vector potentials is examined
Some estimates concerning the Zeeman effect
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.
On the essential spectrum and eigenvalue asymptotics of certain Schrödinger operators
Estimates for the distribution of the first exit time of α-stable processes
The Varopoulos-Hardy-Littlewood theory and the spectral analysis are used to estimate the tail of the distribution of the first exit time of α-stable processes.
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