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  - 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  -