生例1在性空间 y(1)微分运算D是一个线性变换 P=a3x+a2x+a1x+a∈l x Dp=3a3x4+2arx+a1, b3x +h2x +b,x+bo ∈x Dg=3b3x+2b2x+b1, 从而D(p+q) 工工工 =D(a3+b3)x3+(a2+b2)x2+(a1+b1)x+(a0+b0 =3(a3+b)x2+2(a2+b2)x+(a1+b1) =(3a3x2+2a2x+a1)+(3b3x2+2b2x+b) Dp + DqE 上页  , 例 1 在线性空间P4 x 中 (1) 微分运算D是一个线性变换.  , 1 0 4 2 2 3 3  p = a x + a x + a x + a  P x 3 2 , 2 1 2 Dp = a3 x + a x + a  , 1 0 4 2 2 3 3 q = b x + b x + b x + b  P x 3 2 , 2 1 2 Dq = b3 x + b x + b [( ) ( ) ( ) ( )] 1 1 0 0 2 2 2 3 = D a3 + b3 x + a + b x + a + b x + a + b 从而 D( p + q) 3( ) 2( ) ( ) 2 2 1 1 2 = a3 + b3 x + a + b x + a + b (3 2 ) (3 2 ) 2 1 2 2 1 3 2 = a3 x + a x + a + b x + b x + b = Dp + Dq;