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For any positive integer 2 n  and any positive integer  m ,  l , a class of regular self-adjoint and non-self-adjoint boundary value problems whose spectrum consists of at mosteigenvalues is constructed. The key to this analysis is the division of intervals and an iterative construction of the characteristic function. In the self-adjoint case with separated boundary conditions this upper bound can be improved to

Finite Spectrum of 2 n th Order Boundary Value Problems with Transmission Conditions