Trace formulae and inverse spectral theory for Schrödinger operators

Abstract

We extend the well-known trace formula for Hill’s equation to general one-dimensional Schrödinger operators. The new function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="xi"> <mml:semantics> <mml:mi> ξ </mml:mi> <mml:annotation encoding="application/x-tex">\xi</mml:annotation> </mml:semantics> </mml:math> </inline-formula> , which we introduce, is used to study absolutely continuous spectrum and inverse problems.