6 citations · 16 across the 7 of their papers we have counts for
11 papers · 1 filter
(Weak) Hardy and Poincaré inequalities and criticality theory
Marcel Schmidt
In this paper we study Hardy and Poincaré inequalities and their weak versions for quadratic forms satisfying the first Beurling-Deny criterion. We employ these inequalities to est…
On Liouville theorems for Dirichlet forms
Bobo Hua, Matthias Keller, Daniel Lenz +1
We study harmonic functions for general Dirichlet forms. First we review consequences of Fukushima's ergodic theorem for the harmonic functions in the domain of the gener…
A note on the surjectivity of operators on vector bundles over discrete spaces
Jannis Koberstein, Marcel Schmidt
In this note we give a short and self-contained proof for a criterion of Eidelheit on the solvability of linear equations in infinitely many variables. We use this criterion to stu…
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…