3 citations · 5 across the 4 of their papers we have counts for
6 papers
Boundary representations of intermediate forms between a regular Dirichlet form and its active main part
Matthias Keller, Daniel Lenz, Marcel Schmidt +2
We characterize all semigroups sandwiched between the semigroup of a Dirichlet form and the semigroup of its active main part. In case the Dirichlet form is regular, we give a more…
Sobolev-Type Inequalities and Eigenvalue Growth on Graphs with Finite Measure
Bobo Hua, Matthias Keller, Michael Schwarz +1
In this note we study the eigenvalue growth of infinite graphs with discrete spectrum. We assume that the corresponding Dirichlet forms satisfy certain Sobolev-type inequalities an…
A note on Neumann problems on graphs
Michael Hinz, Michael Schwarz
We discuss Neumann problems for self-adjoint Laplacians on (possibly infinite) graphs. Under the assumption that the heat semigroup is ultracontractive we discuss the unique solvab…
Courant's Nodal Domain Theorem for Positivity Preserving Forms
Matthias Keller, Michael Schwarz
We introduce a notion of nodal domains for positivity preserving forms. This notion generalizes the classical ones for Laplacians on domains and on graphs. We prove the Courant nod…
Boundary representation of Dirichlet forms on discrete spaces
Matthias Keller, Daniel Lenz, Marcel Schmidt +1
We describe the set of all Dirichlet forms associated to a given infinite graph in terms of Dirichlet forms on its Royden boundary. Our approach is purely analytical and uses form…
The Kazdan-Warner equation on canonically compactifiable graphs
Matthias Keller, Michael Schwarz
We study the Kazdan-Warner equation on canonically compactifiable graphs. These graphs are distinguished as analytic properties of Laplacians on these graphs carry a strong resembl…