R/2πZ !R ∑ ∑ tχ = tχ + tχ + ··· + tχ + tχ + tχ + ··· + tχ + tχ Dn even Dn

R/2πZ
t
ÈR
„ Dn =
m
eikt =
|k|
tχ
|k|
n
= tχn + tχ
k
n−1
+ ··· + tχ + tχ + tχ
1
0
−1
+ ··· + tχ
1−n
+ tχ−n
n
−t
t
Dn = Dn even
F −t
D
t
t
Dn = Dn = Dn
−π|π
0|π
t
t
Dn = 1 =
t/2π
t/π
−π|π
−π|π
t
tχ
Dn =
|k|
t/2π
k
n t/2π
2t
Dn =
|t|
2it k
e2ikt =
0
k
n
e =
0
k
n
Dn
0
=
|k|
δk = 1
n
(2n + 1) t
s
t
π/2
1 − 2iten + 1
1 − 2it (n + 1)e
=
=
1 − 2ite
1 − 2ite
s
−it
t
e − i (2n + 1) te
c − its − (2n + 1) tc − i(2n + 1) ts
=
−it
−2its
e − ite
t
e−2ikt =
0
k
n
c + its − (2n + 1) tc + i(2n + 1) ts
2its
c − its − (2n + 1) tc − i(2n + 1) ts tc + its − (2n + 1) tc + i(2n + 1) ts
+
−2its
2its
t
2t
e2ikt + e−2ikt =
Dn + 1 =
0
k
n
=
2its + 2i(2n + 1) ts
=1+
2its
(2n + 1) t
s
t
s