Johannes F. Brasche

Weyl function and spectral properties of self-adjoint extensions

We characterize the spectra of self-adjoint extensions of a symmetric operator with equal deficiency indices in terms of boundary values of their Weyl functions. A complete description is obtained for the point and absolutely continuous spectrum while for the singular continuous spectrum additional assumptions are needed. The results are illustrated by examples.

Convergence of Schrödinger Operators

We prove two limit relations between Schrodinger operators perturbed by measures. First, weak convergence of finite real-valued Radon measures

Resolvent Differences for General Obstacles

\mu_n \longrightarrow m

Interactions along Brownian paths in

implies that the operators

Selfadjoint Extensions with Several Gaps: Finite Deficiency Indices

-\Delta + \varepsilon^2 \Delta^2 + \mu_n

On the Approximation of the Solution of the Schrödinger Equation by Superpositions of Stationary Solutions

in

Inverse spectral theory for symmetric operators with several gaps: scalar-type Weyl functions

L^2(\mathbb{R}^d,dx)

Sharp estimates for large coupling convergence with applications to Dirichlet operators

converge to

Dynkin's formula and large coupling convergence

-\Delta + \varepsilon^2 \Delta^2 + m

The Friedrichs Extension of the Aharonov–Bohm Hamiltonian on a Disc

in the norm-resolvent sense, provided