This matrix appears again and again in quantum many body theory. I don't know how to find its eigenvalues.

Imagine a "matrix" M whose components are: M_{x,x'} = u(x)G(x-x') where u and G are complex valued functions of integers x and x'. M is an infinite dimensional matrix. Please tell me what are its eigenvalues for a general u and G (assume any regularity conditions that you desire).

  • $\begingroup$ Don't you think, that is a bit too general a specification to result in specific eigenvalues? $\endgroup$ – mvw Jan 7 '18 at 15:16
  • $\begingroup$ The eigenvalues are function(al)s of u and G $\endgroup$ – Quasar Supernova Jan 7 '18 at 15:17

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