OAI/MathematicalPhysics/DefocusingNLS/Profile/ProfileZeroCriterion.lean

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5 declarations, 0 contain sorry, 0 declared as axioms

Brouwer's theorem applied to the specific certified central linear map.

  1. theorem OAI.DefocusingNLS.ProfileCertificate.central_linear_injective line 9
  2. def OAI.DefocusingNLS.ProfileCertificate.centralLinearEquiv line 17
  3. theorem OAI.DefocusingNLS.ProfileCertificate.centralLinearEquiv_apply line 21
  4. theorem OAI.DefocusingNLS.ProfileCertificate.centralLinearEquiv_inverse_bound line 24
  5. theorem OAI.DefocusingNLS.ProfileCertificate.zero_of_free_profile_error line 34

    Source documentation

    The precise error margin needed to force a zero on the free-profile disk. Continuity and the approximation are hypotheses on a finite-dimensional map, not assumed statements about the NLS or its profiles.

    theorem zero_of_free_profile_error
    (f : Metric.closedBall (0 : ℂ) (radius : ℝ) → ℂ) (hf : Continuous f)
    (herror : ∀ z, ‖f z-realLinearMap centralX centralY z.val‖ ≤ 25/1000000000000) :
    ∃ z, f z = 0 := by
…

    Mentions: OAI.DefocusingNLS.ProfileCertificate.radius, OAI.DefocusingNLS.ProfileCertificate.realLinearMap, OAI.DefocusingNLS.ProfileCertificate.centralX, OAI.DefocusingNLS.ProfileCertificate.centralY