Theorems · Theorem · functional analysis
spectrum.hasDerivAt_resolvent
Deprecated since 2026-03-26Use spectrum.hasDerivAt_resolvent_const_left instead.
∀ {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) kAlias of spectrum.hasDerivAt_resolvent_const_left.
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- Foundations
- Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- NontriviallyNormedFieldstatement · cited by 8,742
- CompleteSpacestatement · cited by 2,532
- NormedAlgebrastatement · cited by 1,165
- NormedRingstatement · cited by 924
- HasDerivAtstatement · cited by 493
- resolventSetstatement · cited by 30
- resolventstatement · cited by 23
- spectrum.hasDerivAt_resolvent_const_leftproof · cited by 3
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