TY  - JOUR
A1  - Beckus, Siegfried
A1  - Eliaz, Latif
T1  - Eigenfunctions growth of R-limits on graphs
JF  - Journal of spectral theory / European Mathematical Society
N2  - A characterization of the essential spectrum of Schrodinger operators on infinite graphs is derived involving the concept of R-limits. This concept, which was introduced previously for operators on N and Z(d) as "right-limits," captures the behaviour of the operator at infinity. For graphs with sub-exponential growth rate, we show that each point in sigma(ss)(H) corresponds to a bounded generalized eigenfunction of a corresponding R-limit of H. If, additionally, the graph is of uniform sub-exponential growth, also the converse inclusion holds.
KW  - Essential spectrum
KW  - Schrodinger operators
KW  - graphs
KW  - right limits
KW  - generalized eigenfunctions
Y1  - 2021
U6  - https://doi.org/10.4171/JST/389
SN  - 1664-039X
SN  - 1664-0403
VL  - 11
IS  - 4
SP  - 1895
EP  - 1933
PB  - EMS Press, an imprint of the European Mathematical Society - EMS - Publishing House GmbH, Institut für Mathematik, Technische Universität
CY  - Berlin
ER  - 
TY  - JOUR
A1  - Beckus, Siegfried
A1  - Pinchover, Yehuda
T1  - Shnol-type theorem for the Agmon ground state
JF  - Journal of spectral theory
N2  - LetH be a Schrodinger operator defined on a noncompact Riemannianmanifold Omega, and let W is an element of L-infinity (Omega; R). Suppose that the operator H + W is critical in Omega, and let phi be the corresponding Agmon ground state. We prove that if u is a generalized eigenfunction ofH satisfying vertical bar u vertical bar <= C-phi in Omega for some constant C > 0, then the corresponding eigenvalue is in the spectrum of H. The conclusion also holds true if for some K is an element of Omega the operator H admits a positive solution in (Omega) over bar = Omega \ K, and vertical bar u vertical bar <= C psi in (Omega) over bar for some constant C > 0, where psi is a positive solution of minimal growth in a neighborhood of infinity in Omega. Under natural assumptions, this result holds also in the context of infinite graphs, and Dirichlet forms.
KW  - Shnol theorem
KW  - Caccioppoli inequality
KW  - Schrodinger operators
KW  - generalized eigenfunction
KW  - ground state
KW  - positive solutions
KW  - weighted
KW  - graphs
Y1  - 2020
U6  - https://doi.org/10.4171/JST/296
SN  - 1664-039X
SN  - 1664-0403
VL  - 10
IS  - 2
SP  - 355
EP  - 377
PB  - EMS Publishing House
CY  - Zürich
ER  - 
TY  - GEN
A1  - Evans, Myfanwy E.
A1  - Hyde, Stephen T.
T1  - Symmetric Tangling of Honeycomb Networks
T2  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe
N2  - Symmetric, elegantly entangled structures are a curious mathematical construction that has found their way into the heart of the chemistry lab and the toolbox of constructive geometry. Of particular interest are those structures—knots, links and weavings—which are composed locally of simple twisted strands and are globally symmetric. This paper considers the symmetric tangling of multiple 2-periodic honeycomb networks. We do this using a constructive methodology borrowing elements of graph theory, low-dimensional topology and geometry. The result is a wide-ranging enumeration of symmetric tangled honeycomb networks, providing a foundation for their exploration in both the chemistry lab and the geometers toolbox.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 1282 
KW  - tangles
KW  - knots
KW  - networks
KW  - periodic entanglement
KW  - molecular weaving
KW  - graphs
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-570842
SN  - 1866-8372
IS  - 1282
ER  - 
TY  - JOUR
A1  - Evans, Myfanwy E.
A1  - Hyde, Stephen T.
T1  - Symmetric Tangling of Honeycomb Networks
JF  - Symmetry
N2  - Symmetric, elegantly entangled structures are a curious mathematical construction that has found their way into the heart of the chemistry lab and the toolbox of constructive geometry. Of particular interest are those structures—knots, links and weavings—which are composed locally of simple twisted strands and are globally symmetric. This paper considers the symmetric tangling of multiple 2-periodic honeycomb networks. We do this using a constructive methodology borrowing elements of graph theory, low-dimensional topology and geometry. The result is a wide-ranging enumeration of symmetric tangled honeycomb networks, providing a foundation for their exploration in both the chemistry lab and the geometers toolbox.
KW  - tangles
KW  - knots
KW  - networks
KW  - periodic entanglement
KW  - molecular weaving
KW  - graphs
Y1  - 2022
U6  - https://doi.org/10.3390/sym14091805
SN  - 2073-8994
VL  - 14
SP  - 1
EP  - 13
PB  - MDPI
CY  - Basel, Schweiz
ET  - 9
ER  -