TY - JOUR
T1 - Electromagnetic Schrödinger Operators on Periodic Graphs with General Conditions at Vertices
AU - Rabinovich, V.
N1 - Publisher Copyright:
© 2019, Pleiades Publishing, Ltd.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - The main aim of the paper is the study of the Fredholm property and essential spectra of electromagnetic Schrödinger operators H on graphs periodic with respect to a group G isomorphic to ℤk. We consider the Schrödinger operators with nonperiodic electric and magnetic potentials and with general nonperiodic conditions on the vertices.We associate with H a family Lim(H) of limit operators Hh generated by sequences h: G ∍hm → ∞. The main results of the paper are: (i) H is a Fredholm operator if and only if all limit operators Hh of H are invertible, (ii) (Formula Presented.) where spessH is the essential spectrum of H. Formula (1) is applied to the study of the essential spectrum of Schrödinger operators whose potentials are perturbations of periodic magnetic and electric potentials by slowly oscillating terms.
AB - The main aim of the paper is the study of the Fredholm property and essential spectra of electromagnetic Schrödinger operators H on graphs periodic with respect to a group G isomorphic to ℤk. We consider the Schrödinger operators with nonperiodic electric and magnetic potentials and with general nonperiodic conditions on the vertices.We associate with H a family Lim(H) of limit operators Hh generated by sequences h: G ∍hm → ∞. The main results of the paper are: (i) H is a Fredholm operator if and only if all limit operators Hh of H are invertible, (ii) (Formula Presented.) where spessH is the essential spectrum of H. Formula (1) is applied to the study of the essential spectrum of Schrödinger operators whose potentials are perturbations of periodic magnetic and electric potentials by slowly oscillating terms.
UR - http://www.scopus.com/inward/record.url?scp=85066792802&partnerID=8YFLogxK
U2 - 10.1134/S1061920819020067
DO - 10.1134/S1061920819020067
M3 - Artículo
SN - 1061-9208
VL - 26
SP - 185
EP - 205
JO - Russian Journal of Mathematical Physics
JF - Russian Journal of Mathematical Physics
IS - 2
ER -