  The purpose of this work is to study spectral methods to approximate the
eigenvalues of nonlocal integral operators. Indeed, even if the spatial domain
is an interval, it is very challenging to obtain closed analytical expressions
for the eigenpairs of peridynamic operators. Our approach is based on the weak
formulation of eigenvalue problem and we consider as orthogonal basis to
compute the eigenvalues a set of Fourier trigonometric or Chebyshev
polynomials. We show the order of convergence for eigenvalues and
eigenfunctions in $L^2$-norm, and finally, we perform some numerical
simulations to compare the two proposed methods.
