TY - JOUR
T1 - On the Decomposition of the Laplacian on Metric Graphs
AU - Breuer, Jonathan
AU - Levi, Netanel
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - We study the Laplacian on family preserving metric graphs. These are graphs that have a certain symmetry that, as we show, allows for a decomposition into a direct sum of one-dimensional operators whose properties are explicitly related to the structure of the graph. Such decompositions have been extremely useful in the study of Schrödinger operators on metric trees. We show that the tree structure is not essential, and moreover, obtain a direct and simple correspondence between such decompositions in the discrete and continuum case.
AB - We study the Laplacian on family preserving metric graphs. These are graphs that have a certain symmetry that, as we show, allows for a decomposition into a direct sum of one-dimensional operators whose properties are explicitly related to the structure of the graph. Such decompositions have been extremely useful in the study of Schrödinger operators on metric trees. We show that the tree structure is not essential, and moreover, obtain a direct and simple correspondence between such decompositions in the discrete and continuum case.
UR - http://www.scopus.com/inward/record.url?scp=85077191132&partnerID=8YFLogxK
U2 - 10.1007/s00023-019-00879-z
DO - 10.1007/s00023-019-00879-z
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AN - SCOPUS:85077191132
SN - 1424-0637
VL - 21
SP - 499
EP - 537
JO - Annales Henri Poincare
JF - Annales Henri Poincare
IS - 2
ER -