2026 | Boundary representations of intermediate forms between a regular Dirichlet form and its active main part | Keller, Matthias; Lenz, Daniel; Schmidt, Marcel; Schwarz, Michael; Wirth, MelchiorZeitschrift: Potential Anal.Band: 64Link zur Publikation
,
Link zum Preprint
Boundary representations of intermediate forms between a regular Dirichlet form and its active main part
Autoren: Keller, Matthias; Lenz, Daniel; Schmidt, Marcel; Schwarz, Michael; Wirth, Melchior
(2026)
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 explicit description of the quadratic forms of the sandwiched semigroups in terms of pairs consisting of an open set and a measure on an abstract boundary.
Zeitschrift:
Potential Anal.
2020 | Courant's Nodal Domain Theorem for Positivity Preserving Forms | Matthias Keller, Michael SchwarzZeitschrift: Journal of Spectral TheorySeiten: 271–309Band: 10Link zur Publikation
,
Link zum Preprint
Courant's Nodal Domain Theorem for Positivity Preserving Forms
Autoren: Matthias Keller, Michael Schwarz
(2020)
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 nodal domain theorem in this generalized setting using purely analytical methods.
Zeitschrift:
Journal of Spectral Theory
2019 | Boundary representation of Dirichlet forms on discrete spaces | Matthias Keller, Daniel Lenz, Marcel Schmidt, Michael SchwarzZeitschrift: Journal de Mathématique Pure et AppliquéeSeiten: 109-143Band: 126Link zur Publikation
,
Link zum Preprint
Boundary representation of Dirichlet forms on discrete spaces
Autoren: Matthias Keller, Daniel Lenz, Marcel Schmidt, Michael Schwarz
(2019)
We describe the set of all Dirichlet forms associated to a given infinitegraphin terms of Dirichlet forms on its Royden boundary. Our approach is purely analyticaland uses form methods.
Zeitschrift:
Journal de Mathématique Pure et Appliquée
2018 | The Kazdan-Warner equation on canonically compactifiable graphs | Keller, Matthias; Schwarz, MichaelZeitschrift: Calc. Var. Partial Differential EquationsSeiten: 18 pp.Band: 57Link zur Publikation
,
Link zum Preprint
,
The Kazdan-Warner equation on canonically compactifiable graphs
Autoren: Keller, Matthias; Schwarz, Michael
(2018)
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 resemblance to Laplacians on open pre-compact manifolds.
Zeitschrift:
Calc. Var. Partial Differential Equations