OAI/MathematicalPhysics/DefocusingNLS/Linear/HomogeneousResolventMoments.lean

GitHub source file

8 declarations, 0 contain sorry, 0 declared as axioms

Power decay on the range of the resolvent contour operator

Resolvent moments satisfy the exact recurrence obtained by multiplying by the time-step operator. A circle of radius less than one therefore gives a geometric estimate on these moments and on powers applied to the contour range.

  1. theorem OAI.DefocusingNLS.operator_mul_resolvent line 21
  2. def OAI.DefocusingNLS.circleResolventMoment line 30
  3. theorem OAI.DefocusingNLS.circleResolventMoment_zero line 35
  4. theorem OAI.DefocusingNLS.circleResolventMoment_succ line 39
  5. theorem OAI.DefocusingNLS.pow_mul_circleResolventOperator line 74
  6. theorem OAI.DefocusingNLS.circleResolventMoment_norm_bound line 82
  7. theorem OAI.DefocusingNLS.pow_mul_circleResolventOperator_norm_bound line 108
  8. theorem OAI.DefocusingNLS.powers_on_circleResolvent_fixedSpace line 116