Find the non-zero e-values and corresponding e-functions of a linear integral operator A with kernel
.This operator acts on the space of continuous functions
in the usual way;
No one knows how to do it even at the tutorials, and the lecturer don't wanna know lol. Help please
If the kernel is defined for x and y lying between 1 and 2, then the integral must go from 1 to 2 (not from 0 to 1), and the function space L must also consist of functions defined on [1,2], not [0.1].
Originally Posted by Elite
If is an eigenvalue then , so . But as far as the integral is concerned, x is a constant, so we can take out the factor and get . But then the integral is a constant, and we are left with two possibilities. The first is that and the integral are both 0. The second is that f(x) is a nonzero constant times , in which case you can plug that formula for f into the integral, and you should then find that (if I've done the integration correctly).
Yep i agree, either there was a mistake in the actual question about the limits or you made a typo while copying.
This question is actually much simpler than the similar types of questions your probably able to do.
the problem here was the 1/x im guessing. but noticing that the function is seperable
you can do it in no time.