(' 22)
PAGE , ' - , "
11 (' 1)
11.1.1 (' 2)
11.1.2 (' 3)
11.1.3 (' 4)
21.1.4/ /
22 (' 5)
22.1.1 (' 6)
22.2 (' 8)
22.2.1
22.2.2
22.2.3 (' 9)
22.2.4
22.2.5
22.2.6 (' 10)
22.2.7
22.2.8
22.2.9
22.2.10 (' 14)
22.2.11 (' 15)
22.3
22.3.1
22.3.2
22.4 (' 16)
22.4.1 ( )
22.4.2 (' 17)
22.4.3 ( 1)
22.5
22.5.1 (' 18)
22.5.2
22.5.3 (' 22)
22.5.4
22.6 , (' 27)
22.6.1 (' 26)
22.6.2 ( ' 1)
23 (' 27)
23.1
33.2 (' 28)
33.3 ,
33.3.1 n
33.4 (' 29)
33.5 E
33.6 : Banach Space (' 30)
33.6.1
33.6.2
33.7 (' 31)
33.7.1 (' 32)
34 (' 35)
34.1.1 (' 39)
34.2
34.2.1
34.2.2
35 (' 40)
35.1 (' 41)
35.1.1 Gram-Schmidt
35.1.2 (' 43)
35.2 (' 44)
35.3 S
45.4 (' 45)
45.4.1 (' 46)
45.5 (' 49)
45.5.1
45.5.2 (' 51)
45.5.3 " ( 2)
45.6 (' 52)
45.6.1
46 (' 54)
46.1.1 (' 55)
46.2
46.3 (' 56)
46.3.1
46.4 (' 61)
46.4.1
46.4.2
46.5 (' 63)
56.6, / - Neumann series (' 66)
56.6.1 (' 68)
56.7
56.8 (' 69)
56.9
56.10
56.10.1
56.10.2 (' 71)
56.10.3 ( 4)
57 (' 72)
57.1.1
57.1.2Equicontinuity
57.1.3 Arzela-Ascoli
57.1.4
57.1.5 (' 73)
57.1.6 (' 77)
57.1.7 ( 4)
57.2 (' 80)
57.3 (' 82)
67.4 (' 84)
67.5 " " (' 85)
67.5.1"
67.6 " " (' 87)
67.7 -
67.7.1
1 (' 1) ,
.
:
.
P :
.
a -A:
.
a -A:
.
"A -B" -A - B:
.
.
C -A -B , , C A -B:
. C -A -B, C A-B:
.A -B (disjoint)
.
: -A -B:
.
1.1.1 (' 2)1. :
:
,
:
.
2. :
:
,
:
.3. :
,
4. :
.5.
.6.
.
1.1.2 (' 3) . :- countable. 1:1 - .
- -.
- .- A -B "" 1:1 . A -B - B -A, -B -A.
1.1.3 (' 4) M , L . : . supremum.
infimum.
1.1.4 / / -X -Y:
.
-X , Domain, f. -Y , Range, f.
Y ( ) ,
.
,
.
, 1:1,
.
1:1 (onto) g :
2 (' 5) , X "" () d, d -, :
2.1.1 (' 6) f:
.
f
.
2.2 (' 8)
S, d P. , :2.2.1 - r "
.
2.2.2
.
2.2.3 (' 9)
A " ( r) A.2.2.4
A A.
2.2.5
A A - .- , .- .- .
2.2.6 (' 10)
-.2.2.7
, .2.2.8 , .
2.2.9
M, , M, . :
- M R " R-M .
- ' .- ' .
- ' .
- ' .
2.2.10 (' 14)A -B .
2.2.11 (' 15) R Seperable A -R.
2.3
2.3.1 ( ) .
2.3.2
. :
. . , . S R -R -S.2.4 (' 16)- S R -S -S.- .
- . 2.4.1 ( )
M R, , r - .
- , , (N ).2.4.2 (' 17)
f - " - -.
2.4.3 ( 1)
A S, -f -A -. f , -sup -inf .
2.5 2.5.1 (' 18)
, -
.
.
2.5.2
R (Complete) -R -R.- , . 2.5.3 (' 22) Y (nested) , .
- R " -R .2.5.4
.
.
.
" .
2.6 , (' 27)A ,
.x A
.
A -
. A , .
- A , .
- , -A , .
2.6.1 (' 26)
T :
, (Kernel).
T
.
T :
.
.
2.6.2 ( ' 1)
G . f
y (" ).
.
3 (' 27)
3.1 L :
- " ". :
- :
- :
.
- -"0" -
.
- "" (-x) -
.- " -x". :
, L ( ) , () .
3.2 (' 28)L -L* 1:1 , .
3.3 ,
:
. L , 0, -
.
, .
3.3.1 n n , n+1 .
n ", " ".3.4 (' 29) , , .
3.5 E E, , "" :
.
.
3.6 : Banach Space (' 30)
, E. , .
.
, , , ().
3.6.1 . , .
3.6.2 () " , .
3.7 (' 31)
L
.
-
.
" . , , , '. .3.7.1 (' 32)
, - - - -. - . :
.
:
:
- - - . - , . - , " ", . .4 (' 35)
" ", , E , F, :
E " ". , :
.
.
4.1.1 (' 39)
:
. , :
,
.
4.2 x,y "
. x -y
.
4.2.1 x,y ,
.
4.2.2
5 (' 40) , , .5.1 (' 41)
S, , , .
.
.5.1.1 Gram-Schmidt
, " ".
.
.
5.1.2 (' 43) H " H,
.
- .
- R .
- H , , -
,
-H.
5.2 (' 44)
- 1:1, , " ", :
.
- -.
5.3 S . " -S"
.
S -, -H -S.
.
:
S (": ).5.4 (' 45) U -H :
. .
5.4.1 (' 46)S: , .
,
.
-S ( ) H.
,
.
.5.5 (' 49)
y, -x S, " ":
."" , x-y, -S.
.
5.5.1
: S -H, . . -y -x S, -S.
, H. -
. :
.
- -f,
.
:
.
5.5.2 (' 51)
5.5.3 " ( 2)
S H,
.5.6 (' 52)
.
5.6.1
H, :
.
. :
,
.
6 (' 54)
:
, .6.1.1 (' 55)
a,b , . .
- K square-integrable T . , :
,
.
6.2
.
:
- "" (commutative).- . . - A .
6.3 (' 56)
A .
.
:
.
":
:
A , , A .
6.3.1
, .
, A " ".
, " ".- T H. :
.
6.4 (' 61)
A: () E.B: A, .
6.4.1 , . .
6.4.2 "
. A "
.:
.
A B. :
.
- E -A E, " -
( A E).6.5 (' 63)
:
. , .
, :
:
.
- " :
,:
T , -T .
.
1. ( A) :
.
2. ( " A) . . . ". :
.
, : " "
.
6.6 , / - Neumann series (' 66)
A B,
. , ":
.
.
"".- . , - .6.6.1 (' 68) ,
.
, "
. , , ":
.6.7
.
A , - . .6.8 (' 69)
A
.
A
.
A B
.
6.9
.
.
6.10 5.5.- .- .
6.10.1
Q,P PQ=0.
. PQ=0 QP=0.. , " .
. " , ,
, -R -S.
. "
.
6.10.2 (' 71)
:
.6.10.3 ( 4)
H -
.
.
" A, 0. " , A .7 (' 72)7.1.1 . .
.
7.1.2 Equicontinuity
- , . equicontinuous
7.1.3 Arzela-Ascoli S " " , - equicontinuous.
7.1.4 A , .
, .
7.1.5 (' 73)
- .- .
- .
- .
- ,
.
- .
- B , , T .- .- .
- .
- A H -B H, BA -AB .7.1.6 (' 77) :
:
1. .2. . , , .
3. (), () .4. , .
5. , T
,
6. T H , , ( ).7. . :
.
.
?
.
8. -0.
9. , .
7.1.7 ( 4)
F H. -F .
7.2 (' 80)
(", eigenvalue) A , , :
. " , eigenvector. " , eigenfunction.: A:
.
: A. .
: A. , " A.
, .
, . , ( )
.
T E, -A - .
7.3 (' 82)T -H.. -H (" ),
. ( ), "
.: !7.4 (' 84) :
,
- , .
,
.
. ?
. , :
1. M .2. . .
3. : M , .
-
.
T
,
,
, .
: ""
,
":
.
7.5 " " (' 85)- " ( ).
7.5.1 "
- T ( ), " T ,
. , , ( ' ).
, .7.6 " " (' 87)1. " " .2. " A .3. " ( A ) .
" ( A ) .
4. " .5. " " .
6. ' A .
. A -
.
7. ( ) . 8. T E -A E, -A - .9. " .
10. " -. " .
11. , " , .
7.7 - A H " " -0 ":
,
-v .
v A . A .
7.7.1 A H. -H " A, :
,
" A -.
8
:
- . - . - . - . - , . - , , , . :
:
:
, x,y .
-:
:
. :
-, . : , , :
.
6
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