Theorems · Theorem · functional analysis
spectrum.hasDerivAt_resolvent_const_left
∀ {𝕜 : Type u_1} {A : Type u_2} [inst : NontriviallyNormedField 𝕜] [inst_1 : NormedRing A] [inst_2 : NormedAlgebra 𝕜 A]
[CompleteSpace A] {a : A} {k : 𝕜}, k ∈ resolventSet 𝕜 a → HasDerivAt (resolvent a) (-resolvent a k ^ 2) k- Cited by
- 3 results in Mathlib
- Foundations
- Depth 180 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites26
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- NontriviallyNormedFieldstatement and proof · cited by 8,742
- Algebra.algebraMapproof · cited by 4,706
- mul_oneproof · cited by 3,885
- CompleteSpacestatement and proof · cited by 2,532
- Units.valproof · cited by 1,966
- NormedAlgebrastatement and proof · cited by 1,165
- NormedRingstatement and proof · cited by 924
- map_oneproof · cited by 861
- HasDerivAtstatement and proof · cited by 493
- HasFDerivAtproof · cited by 350
Cited by3
Results whose statement or proof uses this declaration.
- spectrum.nonemptyproof · cited by 8
- MeasureTheory.measurable_resolventproof · cited by 2
- spectrum.hasDerivAt_resolventproof · cited by 0