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C
h
aracterization of t
h
e potential smoot
h
ness of one-dimensional Dirac operator subject to general boundary conditions and its Riesz basis property
详细信息
查看全文
作者:
İl
k
er Arslan
il
k
erarslan@sabanciuniv.edu" class="aut
h
_mail" title="E-mail t
h
e corresponding aut
h
or
关键词:
Dirac operator
;
Potential smoot
h
ness
;
Riesz basis property
刊名:Journal of Mat
h
ematical Analysis and Applications
出版年:2017
出版时间:1 Marc
h
2017
年:2017
卷:447
期:1
页码:84-108
全文大小:472
K
文摘
T
h
e one-dimensional Dirac operator
w
it
h
periodic potential
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subject to periodic, antiperiodic or a general strictly regular boundary condition (
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as discrete spectrums. It is
k
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at, for large enoug
h
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in t
h
e dis
k
centered at
n
of radius 1/2, t
h
e operator
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as exactly t
w
o (periodic if
n
is even or antiperiodic if
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is odd) eigenvalues
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λ
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(counted according to multiplicity) and one eigenvalue
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μ
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b
c
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corresponding to t
h
e boundary condition
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. We prove t
h
at t
h
e smoot
h
ness of t
h
e potential could be c
h
aracterized by t
h
e decay rate of t
h
e sequence
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δ
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γ
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n
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,
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δ
w>
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n
w>
w>
b
c
w>
=
w>
μ
w>
w>
n
w>
w>
b
c
w>
−
w>
λ
w>
w>
n
w>
w>
+
w>
h>
and
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γ
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n
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=
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λ
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w>
n
w>
w>
+
w>
−
w>
λ
w>
w>
n
w>
w>
−
w>
h>
. Furt
h
ermore, it is s
h
o
w
n t
h
at t
h
e Dirac operator
w
it
h
periodic or antiperiodic boundary condition
h
as t
h
e Riesz basis property if and only if
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t="35"
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γ
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n
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≠
0
w>
w>
hy="false">|
w>
δ
w>
w>
n
w>
w>
b
c
w>
hy="false">|
w>
w>
hy="false">|
w>
γ
w>
w>
n
w>
hy="false">|
w>
h>
is finite.
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