Weighted complex physical Stokes bound #
An exponential weight makes the linear Volterra operator small on a fixed finite interval, independent of its length.
theorem
CKN.Leray.regularisedComplexShiftedStokesIntegral_weighted_norm_le
(F : ℝ → ↥ComplexTensorL2)
(T t M lam : ℝ)
(hT : 0 ≤ T)
(ht : t ≤ T)
(hM : 0 ≤ M)
(hlam : 0 < lam)
(hF : ∀ (s : ℝ), 0 ≤ s → s ≤ T → ‖F s‖ ≤ M * Real.exp (lam * s))
:
A tensor path controlled by an exponential weight has a translated Stokes integral controlled by the same weight and the Gamma kernel.