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math-ph2012
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…
math-ph2012
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_…