- #1
Tomer
- 202
- 0
Homework Statement
I'm probably incredibly rusty, but I can't seem to solve this.
I've been given the space V = C[-[itex]\pi,\pi[/itex]] (continous functions on the closed segment) with the next linear transformation:
T(f(x)) = g(x) = [itex]\int_{-\pi}^{\pi}[1+cos(x-t)]f(t)dt[/itex]
I ought to prove that T(V), the range of V, has a finite dimension, and find an appropriate basis.
Homework Equations
Can't really think of any.
The Attempt at a Solution
I'm really simply blocked. How do I start getting the formation of functions in this space? Intuitively it seems like the addition of a certain number with a cos function, but I can't see any way to directly prove it, nor do I really have an obvious basis.
I'm sorry if it's dumb :-)
Thanks a lot,
Tomer.