203. Utilisation de la notion de compacité

(X, T )
X
(X, d)
A(X, d)A X
⇔
R
[a, b] (a, b)
f(a) = f(b)∃c∈(a, b)f0(c)=0

f0(I)
+∞
∞
+∞x∞
k
k
(xn) (X, d)x{xn}∪{x}
f: [a, b]×[c, d]⇒E E f F :x7→ Rb
af(t, x)dt
L1L∞
C(X, Y )X Y
C([0,1],R)
α
I×Omega Ω
Rn
xt=f(t, x)
x(t0) = x0
KRnCk(K)⊂C0(K)
k+α > k0+α0Ck0,α0(K)⊂Ck,α(K)
ΩRnH1(Ω) ⊂L2

C
C
ΩCa∈Ωf∈H(Ω,Ω) f(a) = a
fnf
|f0(a)|61
|f0(a)|= 1 ⇒f∈Aut(Ω)
|f0a)<1| ⇒ fna
On, SOn, Un, SUn
GLn(R)'On×S++
n
GL+
n(R)'SOn×S++ n
GLn(C)'Un×H++
n
GL+
n(C)'SUn×Hn++
D
T SLn(R)'
SOn×D×T
H1
L2−ε∆u+u=f= 0 Ω
f L2L2F H1
H1

−∆u=f(u)u H1
0(Ω) f∈C0(Ω) ∪L∞
E H
H
V
dim(Vn) = pnun
v a(un, v) = l(v)un
u