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Analytic representations satisfy the convergence hypothesis

Lax825748.NecessaryConvergence · concepts/Lax825748/NecessaryConvergence.lean · lax-825748

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    Natural Language Statement

    Theorem

    The generating series of an analytic differential representation satisfies condition (C). A finite family of Lie polynomials acts by analytic vector fields. Applying the factorial estimate to these new fields, and comparing the total factorial with the product of factorials, gives the assertion.

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    Evidence

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    In the paper

    • page 6 of this submission's paper

    Lean source view on GitHub

    1import Lax825748.FactorialEstimate
    2import Lax825748.AnalyticCalculus
    3import Lax825748.ConvergenceHypothesis
    4
    5/-!
    6---
    7title: Analytic representations satisfy the convergence hypothesis
    8type: theorem
    9---
    10The generating series of an analytic differential representation satisfies
    11condition (C). A finite family of Lie polynomials acts by analytic vector
    12fields. Applying the factorial estimate to these new fields, and comparing
    13the total factorial with the product of factorials, gives the assertion.
    14-/
    15
    16noncomputable section
    17
    18namespace Lax825748.NecessaryConvergence
    19
    20open Lax825748.DifferentialRepresentation AnalyticRepresentations
    21
    22axiom convergence {X : Type} {d : ℕ} (R : Representation X d)
    23 (hR : IsAnalytic R) :
    24 ConvergenceHypothesis.Holds (generatingSeries R)
    25
    26end Lax825748.NecessaryConvergence
    27
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