[線代] linear operator

[mqazz1 (無法顯示)]

for each f屬於C[0,1], define L(f) = F,

               x
where F(x) = ∫  f(t)dt         0 <= x <= 1
               0


show that L is a linear operator on C[0, 1] and then

find L(e^x) and L(x^2)


請問這個題目應該怎麼解呢?

謝謝!!

--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 61.228.28.233
※ 編輯: mqazz1          來自: 61.228.28.233        (05/14 18:05)
→ ricestone   :就直接把線性算子那幾個定義套進去就好了
→ ricestone   :L(a*f)=積分a*f(t)dt等等諸如此類的