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  - 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  - Güneysu, Batu
A1  - Keller, Matthias
T1  - Scattering the Geometry of Weighted Graphs
JF  - Mathematical physics, analysis and geometry : an international journal devoted to the theory and applications of analysis and geometry to physics
N2  - Given two weighted graphs (X, b(k), m(k)), k = 1, 2 with b(1) similar to b(2) and m(1) similar to m(2), we prove a weighted L-1-criterion for the existence and completeness of the wave operators W-+/- (H-2, H-1, I-1,I-2), where H-k denotes the natural Laplacian in l(2)(X, m(k)) w.r.t. (X, b(k), m(k)) and I-1,I-2 the trivial identification of l(2)(X, m(1)) with l(2) (X, m(2)). In particular, this entails a general criterion for the absolutely continuous spectra of H-1 and H-2 to be equal.
KW  - Graphs
KW  - Laplacian
KW  - Scattering theory
Y1  - 2018
U6  - https://doi.org/10.1007/s11040-018-9285-1
SN  - 1385-0172
SN  - 1572-9656
VL  - 21
IS  - 3
PB  - Springer
CY  - Dordrecht
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  -