OAI/MathematicalPhysics/DefocusingNLS/Linear/HomogeneousFiniteRankEigen.lean

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Actual eigenvectors for the finite-rank spectral obstruction

Outside the spectrum of the bounded remainder, a zero of the Schur determinant produces a nonzero eigenvector. Its eigenspace injects into the finite-dimensional factor of the perturbation.

  1. theorem OAI.DefocusingNLS.finiteRank_exists_eigenvector_of_det_zero line 21
  2. theorem OAI.DefocusingNLS.finiteRank_spectrum_iff_exists_eigenvector line 46
  3. theorem OAI.DefocusingNLS.finiteRank_finiteDimensional_eigenspace line 64