Birman–Schwinger Principles for Schrödinger Operators with Distributional Potentials Revisited

Abstract Using a generalized Birman–Schwinger principle developed in [31] for operators formally given by $$H_0 + V$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>+</mml:mo> <mml:mi>V</mml:mi> </mml:mrow> </mml:math> and the theory of Sobolev multipliers, we develop Birman–Schwinger principles for the following concrete situations: one-dimensional Schrödinger and massless relativistic Schrödinger operato