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Construction of Isozaki–Kitada modifiers for discrete Schrödinger operators on general lattices
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We consider a scattering theory for difference operators on
ℋ
=
ℓ
2
(
ℤ
d
;
ℂ
n
)
perturbed with a long-range potential
V
:
ℤ
d
→
ℝ
n
. One of the motivating examples is discrete Schrödinger operators on
ℤ
d
-periodic graphs. We construct time-independent modifiers, so-called Isozaki–Kitada modifiers, and we prove that the modified wave operators with the above-mentioned Isozaki–Kitada modifiers exist and that they are complete.
Title: Construction of Isozaki–Kitada modifiers for discrete Schrödinger operators on general lattices
Description:
We consider a scattering theory for difference operators on
ℋ
=
ℓ
2
(
ℤ
d
;
ℂ
n
)
perturbed with a long-range potential
V
:
ℤ
d
→
ℝ
n
.
One of the motivating examples is discrete Schrödinger operators on
ℤ
d
-periodic graphs.
We construct time-independent modifiers, so-called Isozaki–Kitada modifiers, and we prove that the modified wave operators with the above-mentioned Isozaki–Kitada modifiers exist and that they are complete.
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