6 citations · 16 across the 7 of their papers we have counts for
5 papers · 1 filter
On the uniqueness class, stochastic completeness and volume growth for graphs
Xueping Huang, Matthias Keller, Marcel Schmidt
In this note we prove an optimal volume growth condition for stochastic completeness of graphs under very mild assumptions. This is realized by proving a uniqueness class criterion…
A generalized conservation property for the heat semigroup on weighted manifolds
Jun Masamune, Marcel Schmidt
In this text we study a generalized conservation property for the heat semigroup generated by a Schrödinger operator with nonnegative potential on a weighted manifold. We establish…
On the existence and uniqueness of self-adjoint realizations of discrete (magnetic) Schrödinger operators
Marcel Schmidt
In this expository paper we answer two fundamental questions concerning discrete magnetic Schrödinger operator associated with weighted graphs. We discuss when formal expressions o…
Topological Poincaré type inequalities and lower bounds on the infimum of the spectrum for graphs
Daniel Lenz, Marcel Schmidt, Peter Stollmann
We study topological Poincaré type inequalities on general graphs. We characterize graphs satisfying such inequalities and then turn to the best constants in these inequalities. In…
Geometric properties of Dirichlet forms under order isomorphisms
Daniel Lenz, Marcel Schmidt, Melchior Wirth
We study pairs of Dirichlet forms related by an intertwining order isomorphisms between the associated -spaces. We consider the measurable, the topological and the geometric s…