Abstract
The Gelfand–Yaglom formula relates the regularized determinant of a differential operator to the solution of an initial value problem. Here, we develop a generalized Gelfand–Yaglom formula for a Hamiltonian system with Lagrangian boundary conditions in the discrete and continuous settings. Later, we analyze the convergence of the discretized Hamilton–Jacobi operator and propose a lattice regularization for the determinant.
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