Esercizi svolti di analisi reale e complessa - Dipartimento di ...

•
y(t, β) = e βt .
⎧
⎨
x(t, β) = β tg π
4 t
⎩
y(t, β) = eβt .
Iβ = (−2, 2) ,
β
K R \ {0}
β, β ′ ∈ K C ∩β∈KIβ = (−2, 2) t0 ∈ C
T ≡ sup tg
t∈C
π
4 t
< ∞
M ≡ sup
(β,t)∈K×C
e βt < ∞
B ≡ sup |t| < ∞ .
t∈C
|x(t0, β) − x(t0, β ′ )| ≤
βtg
π
4 t0
≤ T |β − β ′ |
|y(t0, β) − y(t0, β ′ )| ≤
− β ′ tg
e βt0 − e β′
t0
≤
≤ M |βt0 − β ′ t0| ≤
≤ M B |β − β ′ | .
L = T 2 + M 2 B 2 .
π
4 t0
≤
∀ε > 0 ∃N0 ∀m, n >
N0