Ben-Artzi, Matania; Devinatz, Allen The limiting absorption principle for partial differential operators. (English) Zbl 0624.35068 Mem. Am. Math. Soc. 364, 70 p. (1987). From the authors’ abstract: Let H be a self-adjoint operator in a Hilbert space H. It is said to satisfy the “limiting absorption principle” (l.a.p.) in \(U\subset {\mathbb{R}}\) if the limits \(R^{\pm}(\lambda)=\lim_{\epsilon \to 0}(H-\lambda \mp i\epsilon)^{- 1}\), \(\lambda\in U\), exists in some operator topology of B(X,Y), \(X\subset H\), \(Y\subset X\). The paper presents a unified abstract approach to the l.a.p. for operators of the form \(H=H_ 0+V\). The spectral measure associated with \(H_ 0\) is assumed to satisfy certain smoothness assumptions which yields the l.a.p. The perturbation V is assumed to be short-range with respect to \(H_ 0\) and the l.a.p. is proved, along with the discreteness and finite multiplicity of its eigenvalues embedded in U. Various classes of differential operators are studied as special cases, including Schrödinger operators, generalizations of the Stark Hamiltonian and simply characteristic operators. Reviewer: N.Jacob Cited in 26 Documents MSC: 35P25 Scattering theory for PDEs 47A40 Scattering theory of linear operators 81Q15 Perturbation theories for operators and differential equations in quantum theory 81U05 \(2\)-body potential quantum scattering theory Keywords:self-adjoint operator; Hilbert space; limiting absorption principle; spectral measure; perturbation; Schrödinger operators; Stark Hamiltonian; characteristic operators PDFBibTeX XMLCite \textit{M. Ben-Artzi} and \textit{A. Devinatz}, The limiting absorption principle for partial differential operators. Providence, RI: American Mathematical Society (AMS) (1987; Zbl 0624.35068) Full Text: DOI