TY - CHAP
T1 - Dirac operators on R with general point interactions
AU - Rabinovich, Vladimir
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2020.
PY - 2020
Y1 - 2020
N2 - We consider the Dirac operator on R of the form (Formula Presented) is the regular potential, and (Formula Presented) is the singular potential, δ is the Dirac delta-function, Γ(y)=(γij(y))i,j=1,2 is a 2 × 2-matrix with elements (Formula Presented) is an infinite or finite discrete set. We associate with the formal Dirac operator (Formula Presented) the unbounded operator DQ,A,B in (Formula Presented) defined by the operator (Formula Presented) with regular potential Q and the point interaction conditions: (Formula Presented) where (Formula Presented). We study the self-adjointness of DQ,A,B in L2(R, C2), its Fredholm properties, and the essential spectrum. We consider also the influence of slowly oscillating perturbations of regular potentials of periodic Dirac operators to his essential spectrum.
AB - We consider the Dirac operator on R of the form (Formula Presented) is the regular potential, and (Formula Presented) is the singular potential, δ is the Dirac delta-function, Γ(y)=(γij(y))i,j=1,2 is a 2 × 2-matrix with elements (Formula Presented) is an infinite or finite discrete set. We associate with the formal Dirac operator (Formula Presented) the unbounded operator DQ,A,B in (Formula Presented) defined by the operator (Formula Presented) with regular potential Q and the point interaction conditions: (Formula Presented) where (Formula Presented). We study the self-adjointness of DQ,A,B in L2(R, C2), its Fredholm properties, and the essential spectrum. We consider also the influence of slowly oscillating perturbations of regular potentials of periodic Dirac operators to his essential spectrum.
KW - Dirac operators
KW - Essential spectrum
KW - Fredholmness
KW - Point interactions
KW - Self-adjointness
UR - http://www.scopus.com/inward/record.url?scp=85090664654&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-44651-2_21
DO - 10.1007/978-3-030-44651-2_21
M3 - Capítulo
AN - SCOPUS:85090664654
T3 - Operator Theory: Advances and Applications
SP - 351
EP - 381
BT - Operator Theory
PB - Springer
ER -