(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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]

2. Relevant equations

[itex] \lambda x= Kx [/itex]

3. 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?

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Eigenvalues for integral operator

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