Problems Connected with Discrete Spectra
When a vibration is created in a finite structure, its energy may be divided into a set of well-defined vibrations that are called modes of the system. The mathematical model is usually the spectral problem of a linear operator. The modes are then associated with eigenvalues and eigenfunctions (e.g., vibrating strings, etc.). A “continuous extension” of these problems is observed in scattering studies (see chapter II). There are linear operators showing a discrete spectrum, a continuous spectrum, and an exceptional spectrum; and there are also nonlinear systems exhibiting a generalized discrete spectrum. However, we shall stay with the “generic” (most simple) cases and their relations to quantum inverse scattering.
KeywordsInverse Problem Spectral Function Discrete Spectrum Spectral Problem Inverse Spectral Problem
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