Spectral Deformation Theory

  • P. D. Hislop
  • I. M. Sigal
Part of the Applied Mathematical Sciences book series (AMS, volume 113)


The Aguilar-Balslev-Combes-Simon theory of resonances identifies the resonances of a self-adjoint operator H with the complex eigenvalues of a closed operator H(θ), which is obtained from H by the method of spectral deformation. In this chapter, we present the general theory of spectral deformation. This technique is applicable to many situations in mathematical physics, such as Schrödinger operator theory, quantum field theory, plasma stability theory, and the stability of solutions to certain nonlinear partial differential equations [Si4]. We will discuss the application to Schrödinger operators in Chapter 18.


Vector Field Analytic Vector Ordinary Differential Equation Global Flow Complex Extension 
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Copyright information

© Springer Science+Business Media New York 1996

Authors and Affiliations

  • P. D. Hislop
    • 1
  • I. M. Sigal
    • 2
  1. 1.Department of MathematicsUniversity of Kentucky LexingtonUSA
  2. 2.Department of MathematicsUniversity of TorontoTorontoUSA

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