Matrix representations of fourth order boundary value problems with finite spectrum

In this thesis, we construct a class of fourth order self-adjoint boundary value problems whose spectrum is finite and we show that these class of regular self-adjoint fourth order boundary value problems are equivalent to a certain class of matrix eigenvalue problems. Here "being equivalent" means that they have exactly the same eigenvalues. Such an equivalence was previously known only for the second order case and here we will extend these results to fourth order boundary value problems.