Theorems · Theorem · functional analysis
hasStrictFDerivAt_exp_zero_of_radius_pos
∀ {𝕂 : Type u_1} {𝔸 : Type u_2} [inst : NontriviallyNormedField 𝕂] [inst_1 : NormedRing 𝔸] [CharZero 𝕂]
[inst_3 : NormedAlgebra 𝕂 𝔸] [CompleteSpace 𝔸],
0 < (NormedSpace.expSeries 𝕂 𝔸).radius → HasStrictFDerivAt NormedSpace.exp 1 0The exponential in a Banach algebra 𝔸 over a normed field 𝕂 has strict Fréchet derivative
1 : 𝔸 →L[𝕂] 𝔸 at zero, as long as it converges on a neighborhood of zero.
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 182 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites27
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- TopologicalSpaceproof · cited by 24,529
- Moduleproof · cited by 20,661
- RingHom.idstatement and proof · cited by 18,349
- AddCommGroupproof · cited by 12,871
- ENNRealstatement · cited by 9,879
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- ContinuousLinearMapstatement and proof · cited by 5,352
- mul_oneproof · cited by 3,885
- CompleteSpacestatement and proof · cited by 2,532
- Nat.cast_oneproof · cited by 2,501
- zero_addproof · cited by 2,366
Cited by3
Results whose statement or proof uses this declaration.
- hasStrictDerivAt_exp_zero_of_radius_posproof · cited by 2
- hasFDerivAt_exp_zero_of_radius_posproof · cited by 2
- hasStrictFDerivAt_exp_zeroproof · cited by 1