a***n
发帖数: 3633 | 1 如果知道f \in L_1
而且\int_0^\infty{sin(t)*f(t)dt}=0
\int_0^\infty{cos(t)*f(t)dt}=0
能不能说f=0? | n***p
发帖数: 7668 | 2 当然不行。 比如， f(t)= sin 2t, 0
The problem is sin(t) and cos(t) are not enough to span
the space of all functions in L_1.
【在 a***n 的大作中提到】
: 如果知道f \in L_1
: 而且\int_0^\infty{sin(t)*f(t)dt}=0
: \int_0^\infty{cos(t)*f(t)dt}=0
: 能不能说f=0?
| a***n
发帖数: 3633 | 3 Thanks! I also made a counter example to disprove the argument soon I post
it. But my example is way too tedious than yours.
【在 n***p 的大作中提到】
: 当然不行。 比如， f(t)= sin 2t, 0: The problem is sin(t) and cos(t) are not enough to span
: the space of all functions in L_1.
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