Question

which kernel has finite rank ?

Answer 1

in integral equations
$$x(s)=y(s)+\lambda\int_a^b k(s,t)x(t) dt\\k \in L^2[a,b]$$ which one of listed kernels has finite rank ?
how to show (or proof)?
$$a)k(s,t)=\cos(s+t)\\b)k(s,t)=e^{s+t}\cos(s+t)\\c)k(s,t)=e^{st}$$

Answer 2

Ok I'll try this on noon