TY - JOUR
T1 - Spectral asymptotics for resolvent differences of elliptic operators with δ and δ'-interactions on hypersurfaces
AU - Behrndt, Jussi
AU - Grubb, Gerd
AU - Langer, Matthias
AU - Lotoreichik, Vladimir
N1 - (c) European Mathematical Society
PY - 2015/12/1
Y1 - 2015/12/1
N2 - We consider self-adjoint realizations of a second-order elliptic differential expression on Rn with singular interactions of δ and δ'-type supported on a compact closed smooth hypersurface in Rn. In our main results we prove spectral asymptotics formulae with refined remainder estimates for the singular values of the resolvent difference between the standard self-adjoint realizations and the operators with a δ and δ'-interaction, respectively. Our technique makes use of general pseudodifferential methods, classical results on spectral asymptotics of ψdo's on closed manifolds and Krein-type resolvent formulae.
AB - We consider self-adjoint realizations of a second-order elliptic differential expression on Rn with singular interactions of δ and δ'-type supported on a compact closed smooth hypersurface in Rn. In our main results we prove spectral asymptotics formulae with refined remainder estimates for the singular values of the resolvent difference between the standard self-adjoint realizations and the operators with a δ and δ'-interaction, respectively. Our technique makes use of general pseudodifferential methods, classical results on spectral asymptotics of ψdo's on closed manifolds and Krein-type resolvent formulae.
KW - Krein-type resolvent formulae
KW - pseudodifferential methods
KW - spectral asymptotics
UR - http://www.ems-ph.org/journals/journal.php?jrn=jst
U2 - 10.4171/JST/111
DO - 10.4171/JST/111
M3 - Article
VL - 5
SP - 697
EP - 729
JO - Journal of Spectral Theory
JF - Journal of Spectral Theory
SN - 1664-039X
IS - 4
ER -
