Formulas of Szegő Type for the Periodic Schrödinger Operator
We prove asymptotic formulas of Szegő type for the periodic Schrödinger operator H = - d 2 d x 2 + V in dimension one. Admitting fairly general functions h with h ( 0 ) = 0 , we study the trace of the operator h ( χ ( - α , α ) χ ( - ∞ , μ ) ( H ) χ ( - α , α ) ) and link its subleading behaviour as...
Gespeichert in:
| Veröffentlicht in: | Communications in mathematical physics 2018-03, Vol.358 (2), p.675-704 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Zusammenfassung: | We prove asymptotic formulas of Szegő type for the periodic Schrödinger operator
H
=
-
d
2
d
x
2
+
V
in dimension one. Admitting fairly general functions
h
with
h
(
0
)
=
0
, we study the trace of the operator
h
(
χ
(
-
α
,
α
)
χ
(
-
∞
,
μ
)
(
H
)
χ
(
-
α
,
α
)
)
and link its subleading behaviour as
α
→
∞
to the position of the spectral parameter
μ
relative to the spectrum of
H
. |
|---|---|
| ISSN: | 0010-3616 1432-0916 |
| DOI: | 10.1007/s00220-018-3106-z |