Solution
= Solution
Approximate $h$ uniformly by finite sums $\sum f_j(x)g_j(y)$; their <integral> operators have finite-dimensional range and converge in operator norm, so $T_h$ is compact. If $h(x,y)=0$ for $x\le y$, iterated integration over an ordered simplex gives $\|T_h^n\|\le\|h\|_\infty^n/n!$. Thus $r(T_h)=0$, and compact spectral theory gives $\sigma(T_h)=\{0\}$.