Giai tich phuc
Transcript of Giai tich phuc
-
8/14/2019 Giai tich phuc
1/11
T m t t n i d u n g
S p h c l m t s m r n g h o n h o c a t p s t h c , l m t t r - n g s m v n
g i i p h - n g t r n h i s - c g i i q u y t t r i t v n h n g y u c u k h c c a t o n h c .
C h n h v v y s p h c c v a i t r q u a n t r n g t r o n g t o n h c , c b i t l l n h v c t o n h c
n g d n g .
G i i t c h p h c l m t m n h c n g h i n c u v c c s p h c , n - c h n h t h n h d a
t r n n h n g n h l v n g u y n l c b n m n h n g n g u y n l t r n h b y t r o n g t i u l u n
n y l m t p h n t r o n g s .
N i d u n g c h n h c a t i u l u n n y n h - s a u :
P h n 1 : t r n h b y n g u y n l m u n c c i v n g u y n l b o t o n m i n .
P h n 2 : t r n h b y c c n g d n g c a c c n g u y n l t r n .
D o s h n c h v t i l i u v k h n n g n n t i u l u n c n n h i u k h i m k h u y t . T c g i
r t m o n g n h n - c s g p c a T h y C v c c b n .
Q u i N h n , n g y 0 8 t h n g 0 6 n m 2 0 0 9
B i V n C n h
1
-
8/14/2019 Giai tich phuc
2/11
M c l c
1 N h n g n g u y n l c b n 1
1 . 1 N g u y n l b o t o n m i n . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1 . 2 N g u y n l m u n c c i . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
2
n g d n g 3
2 . 1 N g u y n l a r g u m e n t . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 . 2 B S c h w a r z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 . 3 n h l L i o u v i l l e . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 . 4 n h l c b n c a i s . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 . 5 M t s n g d n g k h c . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2
-
8/14/2019 Giai tich phuc
3/11
-
8/14/2019 Giai tich phuc
4/11
T r l i n h l , n u f Ta c o n s t A j f j Ta c o n s t ( d o n h n x t t r n ) .
G i s M a m x
z P G
j f @ z A j v i G a G @ G .
G i s z
l m t i m t h u c G m j f @ z
A j a M
t E a f z P G g j j f @ z A a M j A z
P E . S u y r a E l t p n g ( d o j f @ z A j l i n t c ) .
T a c n c h n g m i n h E m , t c l z
l i m t r o n g c a G .
G i s z
k h n g l i m t r o n g c a E . K h i t r o n g m i l n c n c a z
p h i c i m z k h n g
t h u c E . S u y r a j f @ z A j < M ( d o n h n g h a E ) . L y v n g t r n t m z
, b n k n h , t r n c
z
0
X j f @ z
0
A j < M . V v y W > H X j z z
0
j < t h j f @ z A j < M .
G i C
l c u n g t r n t r n v n g t r n t m z
, b n k n h n m t r o n g l n c n c a z
0
, t a c
f @ z
A a
I
P
2
0
f
z
C e
i
d
j f @ z
A j a
I
P
2
0
f
z
C e
i
d
a
I
P
C
f
z
C e
i
d C
C n C
f
z
C e
i
d
I
P
H
f
d
C
f
z
C e
i
d C
C n C
f
z
C e
i
d
I
g
e
-
8/14/2019 Giai tich phuc
5/11
2 n g d n g
2 . 1 N g u y n l a r g u m e n t
n h l 2 . 1 . G i s f @ z A c h n h h n h t r o n g m i n G , g i i h n b i - n g c o n g n n g C , t r
r a t i h u h n c c i m t r o n g G , c n t r n C , h m f @ z A c h n h h n h v k h c 0 . K h i t a c
I
P i
C
f
H
@ z A
f @ z A
d z a N P
t r o n g N l s k h n g i m c a f @ z A t r o n g G , P l s c c i m t r o n g G , n g t h i m i k h n g
i m h o c c c i m - c t n h m t s l n b n g b i c a n .
C h n g m i n h . G i s f c c c k h n g i m : b
1
; b
2
; : : : ; b
s
v c c c c c i m : a
1
; : : : ; a
r
.
X t h m
@ z A a
f
H
@ z A
f @ z A
G i s z
0
l k h n g i m c p m c a f @ z A . K h i
f @ z A a a
m
@ z z
0
A
m
C : : : ; a
m
Ta H a @ z z
0
A
m
g @ z A ; g @ z
0
A Ta H
.
f
H
@ z A
f @ z A
a @ l o g f @ x A A
H
a m @ z z
0
A
1
C
g
H
@ z A
g @ z A
V g @ z A Ta H n n
g
0
( z )
g ( z )
c h n h h n h . S u y r a
r e s
z
0
f
H
@ z A
f @ z A
a m :
N u z
0
l c c i m c p k c a f @ z A , t n g t t r n , t a c f @ z A @ z z
0
A
k
a g @ z A c h n h h n h v
k h c 0 t i z
0
. D o
f
H
@ z A
f @ z A
a @ l o g f @ x A A
H
a
k
z z
0
C
g
H
@ z A
g @ z A
S u y r a
r e s
z
0
f
H
@ z A
f @ z A
a k
V v y
I
P i
C
f
H
@ z A
f @ z A
a
z P G
r e s
z
f a N P
3
-
8/14/2019 Giai tich phuc
6/11
2 . 2 B S c h w a r z
n h l 2 . 2 . G i s h m f @ z A c h n h h n h t r o n g h n h t r n n v f j z j
-
8/14/2019 Giai tich phuc
7/11
T r l i p h p c h n g m i n h n h l :
G i s f @ z A l c h n h h n h t r n t o n m t p h n g p h c . L y z
0
PC
.
V f @ z A g i i n i n n j f @ z A j M ; V z PC
. K h i x t n g t r n b n k n h r , t m z
0
, p d n g
c n g t h c ( 1 ) , t a c
j f
H
@ z
0
A j M :
I
P r
2
: P r a
M
r
C h o r 3 I , t a c f
H
@ z
0
A a H t r n C
. i u n y c n g h a f l h n g s t r n C
.
2 . 4 n h l c b n c a i s
n h l 2 . 4 . M i a t h c b c n @ n ! I A h s p h c u c n n g h i m . ( m i n g h i m - c t n h
m t s l n b n g b i c a n )
C h n g m i n h . L y f @ z A a z
n
C z
1
z
n 1
C : : : C a
n
; n ! I . C n c h n g m i n h f @ z A c t n h t m t
n g h i m .
G i s f @ z A k h n g c n g h i m . K h i f @ z A Ta H V z PC
; g @ z A a
I
f @ z A
c h n h h n h t r n C
. M
l i m
z 3 I
j f @ z A j a I A l i m
z 3 I
g @ z A a H
S u y r a t n t i m t s R > H l n s a o c h o k h i j z j ! R , t a c j g @ z A j I .
M t k h c , g c h n h h n h n n V j z j R , t h e o n g u y n l m u n c c i , t a c
j g @ z A j m x
j z j = R
j g @ z A j I
D o , t h e o n h L i o u v i l l e , t a c g l h n g s . T s u y r a f p h i l h m h n g . i u n y v
l v f c b c n ! I . V y f p h i c t n h t m t n g h i m z
1
.
B n g c c h v i t l i f t h e o d n g f @ z A a @ z z
1
A q
n 1
@ z A , t a t i p t c l p l u n c h o q
n 1
@ z A ,
r i l i t c h r a n h t r n . T a c t h v i t l i f d i d n g f @ z A a a @ z z
1
A : : : @ z z
n
A . V y f c
n n g h i m .
2 . 5 M t s n g d n g k h c
n h l 2 . 5 . C h o
f @ z A a a
0
C a
1
z C : : : C a
d
z
d
l m t a t h c k h c h n g s , v a
d
Ta H . K h i c m t s p h c z
0
s a o c h o f @ z
0
A a H .
C h n g m i n h . G i s t r i l i . K h i
I
f @ z A
c x c n h v i m i z , v n l h m g i i t c h .
B n g c c h v i t
f @ z A a a
d
z
d
a
0
a
d
z
d
C : : : C I
t a t h y r n g
l i m
j z j 3 I
I
f @ z A
a H
5
-
8/14/2019 Giai tich phuc
8/11
L y l m t s p h c s a o c h o f @ A Ta H . C h n m t s R d n g l n s a o c h o j z j < R , v
n u j z j ! R t h
I
j f @ z A j
@ I ; S A
2
. V y k h n g t n t i f n h t h .
n h l 2 . 7 . G i s f c h n h h n h t r o n g f j z j R g . t M @ r ; f A a m x
j z j r
j f @ z A j . K h i t a c
T @ r ; f A l o g
+
M @ r ; f A
R C r
R r
T @ R ; f A ; H r < R
C h n g m i n h . D o f c h n h h n h n n k h n g c c c i m , s u y r a N @ r ; f A a H . M T @ r ; f A a
m @ r ; f A . T h e o n h n g h a m , t a c
T @ r ; f A a
I
P
2
0
l o g
+
f
r e
i
d l o g
+
M @ r ; f A
S u y r a b t n g t h c u t i n .
N u M @ r ; f A I t h l o g
+
M @ r ; f A a H t h b t n g t h c t h h a i h i n n h i n n g .
G i s M @ r ; f A > I . T h e o n g u y n l m u n c c i , t n t i ( t h u c b i n ) v z
0
a r e
i
s a o
c h o
j f @ z
0
A j a M @ r ; f A
T a c
l o g
+
M @ r ; f A a l o g
+
j f @ z
0
A j a l o g j f @ z
0
A j
p d n g c n g t h c P o i s s o n - J e n s e n
l o g j f @ z
0
A j a
I
P
2
0
l o g
f
R e
i
R
2
r
2
R
2
P R r o s @ A C r
2
d C
M
= 1
l o g
R @ z a
A
R
2
a z
6
-
8/14/2019 Giai tich phuc
9/11
I
P
2
0
l o g
f
R e
i
R
2
r
2
R
2
P R r o s @ A C r
2
d
R C r
R r
I
P
2
0
l o g
f
R e
i
d a
R C r
R r
T @ R ; f A
n h l 2 . 8 . C h o f @ z A l c h n h q u y , v j f @ z A j M t r o n g h n h t r n j z a j R ; v g i s
r n g f @ a A Ta H . K h i n u c c s z
m
; m a I ; : : : ; n t r o n g h n h t r n j z a j
1
3
R m l m c h o
f @ z
m
A a H t h n s k h n g v - t q u A l o g @ M = j f @ z A j A .
C h n g m i n h . T a c t h g i s r n g a a H . L y z
1
; : : : ; z
n
l c c s p h c s a o c h o f @ z
i
A a H
t r o n g j z j
1
3
R v l y
g @ z A a
f @ z A
n
m = 1
I
z
z
m
K h i g @ z A l c h n h q u y v i j z j R , v t r n j z j a R t a c j z = z
m
j ! Q v i m a I ; : : : ; n . V
v y
j g @ z A j
M
n
m = 1
@ Q I A
a P
n
M
v i j z j a R , v v v y c n g v i j z j < R ( t h e o n g u y n l m u n c c i ) . T r o n g t r n g h p
r i n g i u n y c n g n g c h o z a H . B i v g @ H A a f @ H A n n s u y r a r n g
j f @ H A j P
n
M
v v v y
n
I
l o g P
l o g
M
j f @ H A j
y c h n h l i u c n c h n g m i n h .
N h n x t : M t k t q u y h n c t h t h u c t n h l J e n s e n . N u c c s r
1
; : : : ; r
n
t h u c j z j R m f @ r
m
A a H ; m a I ; : : : ; n . K h i
l o g
R
n
r
1
: : : r
n
a
I
P
2
0
l o g
f
e
i
d
l o g j f @ H A j l o g M l o g j f @ H A j
L y c c s r
1
; : : : ; r
n
t h u c j z j R ; H <
-
8/14/2019 Giai tich phuc
10/11
n h l 2 . 9 . ( n h l b a - n g t r n c a H a d a m a r d )
L y f @ z A l m t h m g i i t c h v c h n h q u y t r o n g h n h v n h k h n R
1
j z j r
3
. L y
r
1
< r
2
< r
3
v t M
1
; M
2
; M
3
l c c i c a j f @ z A j t r n v n g t r n j z j a r
1
; r
2
; r
3
t - n g
n g . K h i
M
l o g ( r
3
= r
1
)
2
M
l o g ( r
3
= r
2
)
1
M
l o g ( r
2
= r
1
)
3
( 2 )
C h n g m i n h . L y ' @ z A a z
f @ z A , t r o n g l m t h n g s s c x c n h s a u . K h i
' @ z A l c h n h q u y t r o n g v n h k h n g i a j z j a a r
1
v j z j a r
3
. V v y c c i c a j ' @ z A j x y
r a t r n b i n c a n g t r n ( t h e o n g u y n l m u n c c i ) , t c l
' @ z A m x
r
1
M
1
; r
3
M
3
:
V v y t r n j z j a r
2
,
j f @ z A j m x
r
1
r
2
M
1
; r
3
r
2
M
3
( 3 )
B y g i t a c h n
a
l o g
M
3
M
1
l o g
r
3
r
1
t h a y v o ( 3 ) ,
M
2
r
2
r
1
M
1
v v v y
M
l o g ( r
3
= r
1
)
2
@ r
2
= r
1
A
l o g ( M
3
= M
1
)
M
l o g ( r
3
= r
1
)
1
a M
l o g ( r
3
= r
2
)
1
M
l o g ( r
2
= r
1
)
3
:
8
-
8/14/2019 Giai tich phuc
11/11
T i l i u t h a m k h o
[ 1 ] S . L a n g C o m p l e x a n a l y s i s ( 4 e d ) . S p r i n g e r , 1 9 9 9 .
[ 2 ] T i t c h m a r s h E . C . T h e t h e o r y o f f u n c t i o n s ( 2 e d ) . O x f o r d , 1 9 3 9 .
9