Theorems · Theorem · functional analysis
Function.HasTemperateGrowth.of_fderiv
∀ {E : Type u_5} {F : Type u_6} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : NormedAddCommGroup F]
[inst_3 : NormedSpace ℝ F] {f : E → F},
Function.HasTemperateGrowth (fderiv ℝ f) →
Differentiable ℝ f → ∀ {k : ℕ} {C : ℝ}, (∀ (x : E), ‖f x‖ ≤ C * (1 + ‖x‖) ^ k) → Function.HasTemperateGrowth f- Cited by
- 4 results in Mathlib
- Foundations
- Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites18
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- RingHom.idstatement · cited by 18,349
- NormedAddCommGroupstatement and proof · cited by 15,752
- NormedSpacestatement and proof · cited by 12,499
- Norm.normstatement and proof · cited by 5,413
- ContinuousLinearMapstatement · cited by 5,352
- Set.univproof · cited by 3,945
- fderivstatement and proof · cited by 398
- Differentiablestatement and proof · cited by 298
- LinearIsometryEquiv.symmproof · cited by 287
- iteratedFDerivproof · cited by 211
- AnalyticOnNhdproof · cited by 206
Cited by4
Results whose statement or proof uses this declaration.
- ContinuousLinearMap.hasTemperateGrowthproof · cited by 8
- Function.HasTemperateGrowth.constproof · cited by 5
- Function.hasTemperateGrowth_norm_sqproof · cited by 3
- Function.HasTemperateGrowth.idproof · cited by 1