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  - 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  -