Resumé
Originalsprog | Engelsk |
---|---|
Tidsskrift | Journal of Mathematical Analysis and Applications |
Vol/bind | 464 |
Udgave nummer | 1 |
Sider (fra-til) | 616-661 |
Antal sider | 46 |
ISSN | 0022-247X |
DOI | |
Status | Udgivet - aug. 2018 |
Fingerprint
Citer dette
}
Resolvent expansion for the Schrödinger operator on a graph with infinite rays. / Ito, Kenichi; Jensen, Arne.
I: Journal of Mathematical Analysis and Applications, Bind 464, Nr. 1, 08.2018, s. 616-661.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › peer review
TY - JOUR
T1 - Resolvent expansion for the Schrödinger operator on a graph with infinite rays
AU - Ito, Kenichi
AU - Jensen, Arne
PY - 2018/8
Y1 - 2018/8
N2 - We consider the Schrödinger operator on a combinatorial graph consisting of a finite graph and a finite number of discrete half-lines, all jointed together, and compute an asymptotic expansion of its resolvent around the threshold 0. Precise expressions are obtained for the first few coefficients of the expansion in terms of the generalized eigenfunctions. This result justifies the classification of threshold types solely by growth properties of the generalized eigenfunctions. By choosing an appropriate free operator a priori possessing no zero eigenvalue or zero resonance we can simplify the expansion procedure as much as that on the single discrete half-line.
AB - We consider the Schrödinger operator on a combinatorial graph consisting of a finite graph and a finite number of discrete half-lines, all jointed together, and compute an asymptotic expansion of its resolvent around the threshold 0. Precise expressions are obtained for the first few coefficients of the expansion in terms of the generalized eigenfunctions. This result justifies the classification of threshold types solely by growth properties of the generalized eigenfunctions. By choosing an appropriate free operator a priori possessing no zero eigenvalue or zero resonance we can simplify the expansion procedure as much as that on the single discrete half-line.
KW - Schrödinger operator
KW - Threshold
KW - Resonance
KW - Generalized eigenfunction
KW - Resolvent expansion
KW - Combinatorial graph
U2 - 10.1016/j.jmaa.2018.04.022
DO - 10.1016/j.jmaa.2018.04.022
M3 - Journal article
VL - 464
SP - 616
EP - 661
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
SN - 0022-247X
IS - 1
ER -