V = C^2[0,1] is defined as the space of twice-differentiable real-valued functions on [0,1].

I'm wondering what it means to be on [0,1]. I think it has to do with the inner product. (i.e. the bounds of integration for the inner product are 0,1).

What would be the most general function from V?

Question

V = C^2[0,1] is defined as the space of twice-differentiable real-valued functions on [0,1].

I'm wondering what it means to be on [0,1]. I think it has to do with the inner product. (i.e. the bounds of integration for the inner product are 0,1).

What would be the most general function from V?

kinggeorge · Answer

To be on [0, 1] means the function is defined for those values.

anonymous · Answer

Yeah, but my problem is that I have find two linearly independent eigenvectors  when my eigenvalue is greater than 0, equal to 0 or less than 0, and where my transformation is T(f) = f'' ... I have no idea how can I link lambda (the eigenvalue) to those functions!

kinggeorge · Answer

Can't help you with that part. Sorry :/

anonymous · Answer

No problem, thanks dough