OAI/Topology/CoarseAssembly/ShiftIndex.lean

GitHub source file

9 declarations, 0 contain sorry, 0 declared as axioms

The index-one compressed bilateral shift

  1. def OAI.CoarseAssembly.Analytic.shiftToeplitz line 11
  2. def OAI.CoarseAssembly.Analytic.shiftToeplitzInverse line 13
  3. theorem OAI.CoarseAssembly.Analytic.bilateralShift_star_apply line 15
  4. theorem OAI.CoarseAssembly.Analytic.shiftToeplitz_apply line 22
  5. theorem OAI.CoarseAssembly.Analytic.shiftToeplitzInverse_apply line 32
  6. theorem OAI.CoarseAssembly.Analytic.shiftToeplitz_right_inverse line 41
  7. theorem OAI.CoarseAssembly.Analytic.shiftToeplitz_surjective line 54
  8. theorem OAI.CoarseAssembly.Analytic.shiftToeplitz_ker line 60

    Source documentation

    The kernel is exactly the last negative Fourier coordinate.

    theorem shiftToeplitz_ker : shiftToeplitz.ker =
    Submodule.span ℂ {lp.single 2 (-1 : ℤ) (1 : ℂ)} := by
…
  9. theorem OAI.CoarseAssembly.Analytic.shiftToeplitz_index line 94