Theorems · Theorem · functional analysis
hasStrictFDerivAt_exp
∀ {𝕂 : Type u_1} {𝔸 : Type u_2} [inst : RCLike 𝕂] [inst_1 : NormedCommRing 𝔸] [inst_2 : NormedAlgebra 𝕂 𝔸]
[CompleteSpace 𝔸] {x : 𝔸}, HasStrictFDerivAt NormedSpace.exp (NormedSpace.exp x • 1) xThe exponential map in a commutative Banach algebra 𝔸 over 𝕂 = ℝ or 𝕂 = ℂ has strict
Fréchet derivative NormedSpace.exp x • 1 : 𝔸 →L[𝕂] 𝔸 at any point x.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idstatement · cited by 18,349
- ContinuousLinearMapstatement · cited by 5,352
- RCLikestatement and proof · cited by 2,829
- CompleteSpacestatement and proof · cited by 2,532
- NormedAlgebrastatement and proof · cited by 1,165
- HasStrictFDerivAtstatement · cited by 261
- NormedCommRingstatement and proof · cited by 218
- NormedSpace.expstatement · cited by 157
- edist_lt_topproof · cited by 32
- NormedSpace.expSeries_radius_eq_topproof · cited by 27
- hasStrictFDerivAt_exp_of_mem_ballproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- hasFDerivAt_expproof · cited by 0