120
17 Examples
||[α
V
t (A), B]|| ≤ ||A||
x
sup
C∈A({0})
(|| [α x (C), B] ||/||C||)e
−|x|λ+2|t| ||Φ|| λ
and the essentially finite velocity of propagation of physical disturbances
||[α x α
V
t (A), B]|| ≤ 2||A|| ||B|| e
−|t|(λ|x|/|t|−2||Φ|| λ )
.
(17.16)
17 Examples
||[α
V
t (A), B]|| ≤ ||A||
x
sup
C∈A({0})
(|| [α x (C), B] ||/||C||)e
−|x|λ+2|t| ||Φ|| λ
and the essentially finite velocity of propagation of physical disturbances
||[α x α
V
t (A), B]|| ≤ 2||A|| ||B|| e
−|t|(λ|x|/|t|−2||Φ|| λ )
.
(17.16)