TY  - JOUR
A1  - Hinz, Michael
A1  - Schwarz, Michael
T1  - A note on Neumann problems on graphs
JF  - Positivity
N2  - 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 solvability for non-empty subgraphs with respect to the vertex boundary and provide analytic and probabilistic representations for Neumann solutions. A second result deals with Neumann problems on canonically compactifiable graphs with respect to the Royden boundary and provides conditions for unique solvability and analytic and probabilistic representations.
KW  - Graphs
KW  - Discrete Dirichlet forms
KW  - Neumann problem
KW  - Royden boundary
Y1  - 2022
U6  - https://doi.org/10.1007/s11117-022-00930-0
SN  - 1385-1292
SN  - 1572-9281
VL  - 26
IS  - 4
PB  - Springer
CY  - Dordrecht
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Schwarz, Michael
T1  - Courant’s nodal domain theorem for positivity preserving forms
JF  - Journal of spectral theory
N2  - 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.
KW  - Nodal domain
KW  - eigenfunction
KW  - Dirichlet form
KW  - compact resolvent
Y1  - 2020
U6  - https://doi.org/10.4171/JST/292
SN  - 1664-039X
SN  - 1664-0403
VL  - 10
IS  - 1
SP  - 271
EP  - 309
PB  - EMS Publishing House
CY  - Zürich
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Schwarz, Michael
T1  - The Kazdan-Warner equation on canonically compactifiable graphs
JF  - Calculus of variations and partial differential equations
N2  - 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.
Y1  - 2018
U6  - https://doi.org/10.1007/s00526-018-1329-7
SN  - 0944-2669
SN  - 1432-0835
VL  - 57
IS  - 2
PB  - Springer
CY  - Heidelberg
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Lenz, Daniel
A1  - Schmidt, Marcel
A1  - Schwarz, Michael
T1  - Boundary representation of Dirichlet forms on discrete spaces
JF  - Journal de Mathématiques Pures et Appliquées
N2  - 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 methods. (C) 2018 Elsevier Masson SAS.
KW  - Dirichlet form
KW  - Royden boundary
KW  - Infinite graph
KW  - Harmonic measure
KW  - Trace Dirichlet form
Y1  - 2019
U6  - https://doi.org/10.1016/j.matpur.2018.10.005
SN  - 0021-7824
SN  - 1776-3371
VL  - 126
SP  - 109
EP  - 143
PB  - Elsevier
CY  - Amsterdam
ER  - 
TY  - THES
A1  - Schwarz, Michael
T1  - Nodal domains and boundary representation for Dirichlet forms
Y1  - 2020
ER  -