122 citations · 452 across the 56 of their papers we have counts for
5 papers · 2 filters
Applications of elliptic operator theory to the isotropic interior transmission eigenvalue problem
Evgeny Lakshtanov, Boris Vainberg
The paper concerns the isotropic interior transmission eigenvalue (ITE) problem. This problem is not elliptic, but we show that, using the Dirichlet-to-Neumann map, it can be reduc…
On the negative spectrum of the hierarchical Schrödinger operator
S. Molchanov, B. Vainberg
This paper is devoted to the spectral theory of the Schrödinger operator on the simplest fractal: Dyson's hierarchical lattice. An explicit description of the spectrum, eigenfuncti…
Bounds on positive interior transmission eigenvalues
Evgeny Lakshtanov, Boris Vainberg
The paper contains lower bounds on the counting function of the positive eigenvalues of the interior transmission problem when the latter is elliptic. In particular, these bounds j…
Non-Random Perturbations of the Anderson Hamiltonian in the 1-D case
J. Holt, S. Molchanov, B. Vainberg
Recently (see Molchanov & Vainberg 2011), two of the authors applied the Lieb method to the study of the negative spectrum for particular operators of the form . Here, $H_…
Bargmann type estimates of the counting function for general Schrödinger operators
S. Molchanov, B. Vainberg
The paper concerns upper and lower estimates for the number of negative eigenvalues of one- and two-dimensional Schrödinger operators and more general operators with the spectral d…