- #1
margaret37
- 12
- 0
Homework Statement
Find all non-zero eignvalues and eigenvectors for the following integral operator
[itex] Kx := \int^{\ell}_0 (t-s)x(s) ds [/itex]
in [itex] C[0,\ell] [/itex]
Homework Equations
[itex] \lambda x= Kx [/itex]
The Attempt at a Solution
[itex] \int^{\ell}_0 (t-s)x(s) ds = \lambda * x(t) [/itex]
[itex] t\int^{\ell}_0 x(s) ds - s\int^{\ell}_0x(s) ds = \lambda * x(t) [/itex]
Am I even going the right direction?
I think I need function(s) of x(t) and scalar [itex] \lambda [/itex], when I am finished is that right?
And should [itex] \lambda [/itex] be a complex (possibly real) number?