We consider magnetic Schrödinger operators on quantum graphs with identical edges. The
spectral problem for the quantum graph is reduced to the discrete magnetic Laplacian on the …

We consider the Laplacian on a periodic metric graph and obtain its decomposition into a
direct fiber integral in terms of the corresponding discrete Laplacian. Eigenfunctions and …

In this paper we define (local) Dirac operators and magnetic Schrödinger Hamiltonians on
fractals and prove their (essential) self-adjointness. To do so we use the concept of 1-forms …

This is an expository article on discrete geometric analysis based on the lectures which the
author gave at Gregynog Hall, University of Wales, as an activity of the Project “Analysis on …

The aim of this expository article is to exhibit several interesting interactions among
geometry, graph theory and probability through a brief survey of a series of our recent work …

We consider magnetic Schrödinger operators with periodic magnetic and electric potentials
on periodic discrete graphs. The spectrum of the operators consists of an absolutely …

Given a (conservative) symmetric Markov process on a metric space we consider related
bilinear forms that generalize the energy form for a particle in an electromagnetic field. We …

We consider a Laplacian on periodic discrete graphs. Its spectrum consists of a finite
number of bands. In a class of periodic 1-forms, ie, functions defined on edges of the …

We consider discrete Schrödinger operators with periodic potentials on periodic graphs
perturbed by guided non-positive potentials, which are periodic in some directions and …

We consider Schrödinger operators with periodic potentials on periodic discrete graphs.
Their spectrum consists of a finite number of bands. We determine trace formulas for the …