Extension of Ambarzumyan’s Theorem to General Boundary Conditions

We extend the classical Ambarzumyan’s theorem for the Sturm–Liouville equation (which is concerned only with Neumann boundary conditions) to the general boundary conditions, by imposing an additional condition on the potential function. Our result supplements the P¨oschel–Trubowitz inverse spectral theory. We also have parallel results for vectorial Sturm–Liouville systems