OAI/MathematicalPhysics/ContinuumCoulomb/OneParticle/ExplicitVerticalCutoff.lean

GitHub source file

7 declarations, 0 contain sorry, 0 declared as axioms

An explicit smooth transverse cutoff. Its formula uses only the fixed smooth transition function, so rational approximation can use the actual exponential formula instead of a classically selected bump function.

  1. def OAI.ContinuumCoulomb.verticalCutoffBump line 13
  2. theorem OAI.ContinuumCoulomb.verticalCutoffBump.contDiff line 18
  3. theorem OAI.ContinuumCoulomb.verticalCutoffBump.nonneg line 21
  4. theorem OAI.ContinuumCoulomb.verticalCutoffBump.le_one line 24
  5. theorem OAI.ContinuumCoulomb.verticalCutoffBump.one_of_mem_closedBall line 27
  6. theorem OAI.ContinuumCoulomb.verticalCutoffBump.zero_of_le_dist line 35
  7. theorem OAI.ContinuumCoulomb.verticalCutoffBump.hasCompactSupport line 43