OAI/MathematicalPhysics/ContinuumCoulomb/OneParticle/LocalizedModeDerivatives.lean

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9 declarations, 0 contain sorry, 0 declared as axioms

Actual classical first derivatives of the localized modes are L2. The planar/transverse product formula and the volume-preserving chart give membership without a smooth-compact-support assumption on the orbitals.

  1. theorem OAI.ContinuumCoulomb.normalizedPlanarMode_partial line 13
  2. theorem OAI.ContinuumCoulomb.normalizedPlanarMode_partial_square_integrable line 19
  3. theorem OAI.ContinuumCoulomb.normalizedPlanarMode_partial_memLp line 24
  4. theorem OAI.ContinuumCoulomb.localizedMode_fderiv line 30
  5. theorem OAI.ContinuumCoulomb.localizedMode_planarDerivative_memLp line 51
  6. theorem OAI.ContinuumCoulomb.localizedMode_verticalDerivative_memLp line 63
  7. theorem OAI.ContinuumCoulomb.localizedMode_fderiv_memLp line 73
  8. theorem OAI.ContinuumCoulomb.continuumLocalizedMode_fderiv line 79
  9. theorem OAI.ContinuumCoulomb.continuumLocalizedMode_fderiv_memLp line 86