台湾国立交通大学 吴培元: 泛函分析讲义

果珍冰

+ ^: \4 D* o2 P, |, X6 R( t! ]課程內容
* H+ a8 a% l, R6 Y: e! n; Q& d' F
Class1
課程介紹與導論
6 k% b1 D2 d* m( i
) h2 r1 {" [9 O0 k3 j
# `2 v  G! h$ u; Z8 U: ~- ]7 sClass2
第一章 Measure theory


Class3
2 T3 e8 [  m" S# uSec.1.2. Measure        
Sec.1.3. Outer Measure
" j: X' @6 ~7 W. D& J1 t, ~, H

Class4
Sec.1.4. Constructing outer measure

( F8 x' _. L1 s0 D. l9 ?0 s
( u% r+ x6 j2 I& U6 e& MClass5
/ a( C5 ~8 H1 ASec.1.5-1.6 Lebesgue measure
  Y: r5 x* p! V  A$ \: k
# e% K2 S) K' n1 ^* |( t: s7 Y
Class6
9 p8 G; _( Q, I' t4 h) cSec.1.7 Metric space


Class7
* q. {" Q6 E! x5 r6 F9 lSec.1.8-1.9 Construction of metric outer measure
5 \; A7 D/ v9 Y0 D

Class8
Sec.1.9 Construction of metric outer measure

: t4 }+ J1 O+ o5 A' l; `
Class9
sec.1.10 Signed measure
# _+ X) n9 j# w( s  C
# A8 y, m- f1 D! S; K6 Z9 o) M
0 O9 v6 V0 `% P! b7 k" MClass10
- x3 n( n* j% v
" A; n. Y, {& t7 [8 h
1 G" K2 K8 X1 ]; |8 Q* tClass11        
4 e, U9 f0 {1 |! W  |1 j' @第二章 Integration
' ~, r" l: k  I5 V) z& r# FSec. 2.2 Operations on measurable functions

7 G! z) t' f& v5 w* @5 _1 e- Y- G
Class12
. r7 |  W+ D% B+ F8 L. X% NSec 2.3. Egoroff’s Thm.
* o; O: b$ h- B0 V0 i$ z

) i" `8 ^/ E. G" IClass13
* X/ b& J+ r2 J/ Z, NSec 2.3 Egoroff’s Thm.

3 ~' z; T6 A7 n: v4 f3 y; O
  B4 u6 r! f1 u* G5 N6 [Class14
" J4 {0 y: o8 b. U" WSec 2.4 Convergence in measure
- Y! q, o5 @9 O! K

Class15
Sec 2.5 Integrals of simple functions

! ?8 X! Y. U. M+ |1 C4 ]
Class16
Sec. 2.6 Integrable functions

& W6 k  S6 s* t
) c, [( K7 E& L  y, mClass17

% ]) w2 n' E  t' `- h
Class18
- a( ?3 }7 T1 @( W) x* W5 X7 u# LSec. 2.7 Properties of integrals
( E# z' A; |' R& B, a' B) A

7 g- g, u; v3 M/ Z0 zClass19-20
; [- P) x0 }) {, P
$ _8 a9 b3 w* }6 s# A) s
Class21
Sec.2.9 DCT
8 V9 W2 z3 z$ K& b$ }

Class22
+ ?0 W( N. V, m  i/ _Sec. 2.10 Applications of DCT
! j$ U$ L( n: J# Y; O2 P
% ^# V" h! r  ?$ N# h
0 J* D# k" w" OClass23-24
8 H6 A, g9 l/ M7 k8 j  jSec 2.11 (Proper) Riemann integral


# u6 x; _7 E; x+ C* k1 j5 xClass25
% ^/ P2 w, ]) j* W- n
. C- a6 d. `; B+ B
, t0 ~4 ]9 q( G, BClass26
Sec. 2.13. Lebesgue decomposition
+ I0 K2 m. k. S1 i& X

6 N7 V; h( r1 r. d0 cClass27
- g+ m$ k5 H" n6 a" @- `( uSec. 2.13. Lebesgue decomposition

- t& m% Q0 }/ d
Class28
; X( K+ S1 Q" H2 O; ]' kSec. 2.14 Fundamental Thm of Calculus on
& c7 j* ]) c0 ?! F

5 m( P$ K5 h; D3 ^+ ]: pClass29
9 _9 W- W5 x& n4 I

( O7 V/ U6 P1 {5 B0 ?% l) \Class30

) m; \" g8 y, Q7 L1 o' b# P' X
5 e5 c1 D0 p$ T+ CClass31

+ T( l1 Q) m! M1 R4 i+ F3 ?
Class32


Class33
第三章 Metric spaces
% F) J1 w  K3 ]/ F9 DSec. 3.1 Topological spaces & metric spaces


Class34
' a6 E2 @" i7 K$ \$ H

Class35
0 {. v( Y! \8 P

Class36


Class37
- R" d  S3 @4 U1 y
2 l0 d+ K! }. \. ?3 S7 Q
2 L2 i7 t; ~" W/ FClass38
4 N0 {( v% i. A

" \" c% V' v+ S) ]! hClass39
# a; U# @" {! ?

6 K5 x& ]1 ~; r% RClass40

' T7 B% z! }4 ~9 o* t+ _$ q9 D# P
Class41
( p9 E8 Z' e: xSec.3.7 Stone-Weierstiass Thm.

% ]+ v: @9 y4 q  f
9 q/ Y7 z3 ?6 B8 @: ]8 |Class42
; [' [7 j1 [- `7 v9 @2 G

Class43

" ]9 k5 \" @. y5 I5 w( u
Class44
" \0 h. {: W4 r8 e$ n第四章 Banach spaces

( O/ ^, H# Z' k. ~" E8 J: v
/ A+ e. x# @7 q5 |% uClass45-46
2 A" g" t9 z, V& cSec. 4.4 Linear Transformations
) W- C  J$ L7 j5 ~* H

  a! |* |2 Y( g6 EClass47
4 Q  v9 Z: R2 h% ^8 qsec. 4.5 Principle of uniform bddness (Banach- Steinhaus Thm)
6 d, {( M/ d; j
; ^' M3 ?! X6 I# K& U, F
# {% q1 g: ?0 D8 }  X) P6 V- pClass48


Class49
2 V5 ~$ B- g7 |1 _/ G
3 f( u* p# @: p+ G( X# H
Class50
2 W' c: R$ R  ^6 ?7 ]

% @" ]+ t- o# G( v& i: K: IClass51 无


Class52

* G& b# Y/ k, ?& T$ J! v0 e$ f' h
Class53
0 x) D- O+ n/ m, L: o6 K$ o. m0 M) q

Class54-56
2 i$ @: U  ?: f+ @* h6 [
) G3 X+ X" L$ }: H/ P7 C
2 P2 E! [# ]9 Y2 G) o$ W) E3 U) AClass57


Class58
, t! {# e( k. LSec. 4.11 Topology
  I0 m) ~& `+ d. G* \

/ \* m) k/ s. j- B9 q' `Class59

% x! U) H/ q5 A; C) j
' ^; `( B# P1 T6 k6 s3 u( J# c( nClass60
, A, f* T' d$ w. mSec. 4.13 Adjoint operators
6 M9 Q5 [* X- X1 V9 N" P+ p
" @# r( b! t8 J- e# Q1 Q
Class61
+ w8 r+ H- {4 p- C$ W
4 R/ L( T' L# t2 `& G% J, H4 P
3 J- \' P8 H+ oClass62
8 f# J7 a# _5 s1 T4 ~( j% G

# D. e: d# [. H) m/ ?Class63


Class64


Class65
7 _; n1 w  X7 I  @第五章 Compact operators
5 d6 F+ ?* D; S8 d/ _$ e% |- P

Class66
Sec. 5.2 Fredholm-Riesz-Schauder Theory


# [9 U) W8 d' H8 sClass67

$ E; e% y- |* [! e0 Z
Class68


" x+ ^& {$ o- C$ J( B" h. KClass69
1 O$ p7 `: K. L, TSec.5.3 Spectral theory



2 |. q1 `& C/ Q. e! B" X7 ^6 ^

数学中国YY主管

台湾同胞的也有啊

小清新——k

希望有用！！！！！！！！！！！！！1111
+ c5 e) t. B" E& _, N. i+ m

pianpian5083

找了很久了
' e) E, v# p* b( V/ a

71895167

网上只缺51讲，不知道这里能不能找到
- ^" f3 Q2 O; R% R$ \5 A