Theorems · Theorem · functional analysis

CFC.log_pow

∀ {A : Type u_1} [inst : NormedRing A] [inst_1 : StarRing A] [inst_2 : NormedAlgebra ℝ A]
  [inst_3 : ContinuousFunctionalCalculus ℝ A IsSelfAdjoint] (n : ℕ) (a : A),
  (∀ x ∈ spectrum ℝ a, x ≠ 0) → autoParam (IsSelfAdjoint a) CFC.log_pow._auto_1 → CFC.log (a ^ n) = n • CFC.log a

Defined in: Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedRing StarRing NormedAlgebra ContinuousFunctionalCalculus

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NormedRingstatement and proof · cited by 924
IsSelfAdjointstatement and proof · cited by 545
spectrumstatement and proof · cited by 510

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