Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator
Estimates for Periodic and Dirichlet Eigenvalues of the Schrödinger Operator
Consider the Schrödinger equation $-y' + Vy = \lambda y$ for a complex-valued potential V of period 1 in the weighted Sobolev space $H^w$ of 2-periodic functions $f : \mathbb R \rightarrow \mathbb C$, \[ H^w \equiv H^w_{\mathbb C}:= \left\{ f(x) = \sum^\infty_{k= -\infty } \hat f(k) e^{i\pi kx} | …