OAI/MathematicalPhysics/ContinuumCoulomb/OneParticle/PlanarModeDerivatives.lean

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13 declarations, 0 contain sorry, 0 declared as axioms

Actual first and second directional derivatives of the resolvent mode. Differentiation is transferred to the compact forcing, which also gives finite L¹ and L² derivatives without differentiating the singular kernel.

  1. theorem OAI.ContinuumCoulomb.planarResolventKernel_nonnegative line 14
  2. def OAI.ContinuumCoulomb.planarResolventOf line 20
  3. theorem OAI.ContinuumCoulomb.planarResolventOf_integrable line 23
  4. theorem OAI.ContinuumCoulomb.planarResolventOf_continuous line 28
  5. theorem OAI.ContinuumCoulomb.planarResolventOf_bound line 33
  6. theorem OAI.ContinuumCoulomb.planarResolventOf_square_integrable line 43
  7. theorem OAI.ContinuumCoulomb.planarResolventOf_partial line 56
  8. theorem OAI.ContinuumCoulomb.planarResolventMode_partial line 74
  9. theorem OAI.ContinuumCoulomb.planarResolventMode_partial_integrable line 79
  10. theorem OAI.ContinuumCoulomb.planarResolventMode_partial_square_integrable line 87
  11. theorem OAI.ContinuumCoulomb.planarResolventMode_partial_partial line 94
  12. theorem OAI.ContinuumCoulomb.planarResolventMode_partial_partial_square_integrable line 103
  13. theorem OAI.ContinuumCoulomb.planarResolventMode_partial_partial_integrable line 110