TY  - JOUR
A1  - Keller, Matthias
A1  - Pinchover, Yehuda
A1  - Pogorzelski, Felix
T1  - From hardy to rellich inequalities on graphs
JF  - Proceedings of the London Mathematical Society
N2  - We show how to deduce Rellich inequalities from Hardy inequalities on infinite graphs. Specifically, the obtained Rellich inequality gives an upper bound on a function by the Laplacian of the function in terms of weighted norms. These weights involve the Hardy weight and a function which satisfies an eikonal inequality. The results are proven first for Laplacians and are extended to Schrodinger operators afterwards.
KW  - 35R02
KW  - 39A12 (primary)
KW  - 26D15
KW  - 31C20
KW  - 35B09
KW  - 58E35 (secondary)
Y1  - 2020
U6  - https://doi.org/10.1112/plms.12376
SN  - 0024-6115
SN  - 1460-244X
VL  - 122
IS  - 3
SP  - 458
EP  - 477
PB  - Wiley
CY  - Hoboken
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Pinchover, Yehuda
A1  - Pogorzelski, Felix
T1  - Criticality theory for Schrödinger operators on graphs
JF  - Journal of spectral theory
N2  - We study Schrodinger operators given by positive quadratic forms on infinite graphs. From there, we develop a criticality theory for Schrodinger operators on general weighted graphs.
KW  - green function
KW  - ground state
KW  - positive solutions
KW  - discrete Schrodinger
KW  - operators
KW  - weighted graphs
Y1  - 2019
U6  - https://doi.org/10.4171/JST/286
SN  - 1664-039X
SN  - 1664-0403
VL  - 10
IS  - 1
SP  - 73
EP  - 114
PB  - European Mathematical Society
CY  - Zürich
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Pinchover, Yehuda
A1  - Pogorzelski, Felix
T1  - Optimal Hardy inequalities for Schrodinger operators on graphs
JF  - Communications in mathematical physics
N2  - For a given subcritical discrete Schrodinger operator H on a weighted infinite graph X, we construct a Hardy-weight w which is optimal in the following sense. The operator H - lambda w is subcritical in X for all lambda < 1, null-critical in X for lambda = 1, and supercritical near any neighborhood of infinity in X for any lambda > 1. Our results rely on a criticality theory for Schrodinger operators on general weighted graphs.
Y1  - 2018
U6  - https://doi.org/10.1007/s00220-018-3107-y
SN  - 0010-3616
SN  - 1432-0916
VL  - 358
IS  - 2
SP  - 767
EP  - 790
PB  - Springer
CY  - New York
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Pinchover, Yehuda
A1  - Pogorzelski, Felix
T1  - An improved discrete hardy inequality
JF  - The American mathematical monthly : an official publication of the Mathematical Association of America
N2  - In this note, we prove an improvement of the classical discrete Hardy inequality. Our improved Hardy-type inequality holds with a weight w which is strictly greater than the classical Hardy weight w(H)(n) : 1/(2n)(2), where N.
KW  - Primary 26D15
Y1  - 2018
U6  - https://doi.org/10.1080/00029890.2018.1420995
SN  - 0002-9890
SN  - 1930-0972
VL  - 125
IS  - 4
SP  - 347
EP  - 350
PB  - Taylor & Francis Group
CY  - Philadelphia
ER  - 
TY  - JOUR
A1  - Keller, Matthias
A1  - Münch, Florentin
A1  - Pogorzelski, Felix
T1  - Geometry and spectrum of rapidly branching graphs
JF  - Mathematische Nachrichten
N2  - We study graphs whose vertex degree tends to infinity and which are, therefore, called rapidly branching. We prove spectral estimates, discreteness of spectrum, first order eigenvalue and Weyl asymptotics solely in terms of the vertex degree growth. The underlying techniques are estimates on the isoperimetric constant. Furthermore, we give lower volume growth bounds and we provide a new criterion for stochastic incompleteness. (C) 2016 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
KW  - Graph Laplacians
KW  - discrete spectrum
KW  - eigenvalue asymptotics
KW  - isoperimetric estimates
KW  - stochastic completeness
Y1  - 2016
U6  - https://doi.org/10.1002/mana.201400349
SN  - 0025-584X
SN  - 1522-2616
VL  - 289
SP  - 1636
EP  - 1647
PB  - Wiley-VCH
CY  - Weinheim
ER  -