Theorems · Definition · complex analysis
Complex.reCLM
ℂ →L[ℝ] ℝ
Continuous linear map version of the real part function, from ℂ to ℝ.
- Defined in
- Mathlib.Analysis.Complex.Basic
- Cited by
- 46 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement · cited by 25,697
- RingHom.idstatement · cited by 18,349
- Complexstatement and proof · cited by 5,565
- ContinuousLinearMapstatement · cited by 5,352
- LinearMap.mkContinuousproof · cited by 9
- Complex.reLmproof · cited by 6
Cited by47
Results whose statement or proof uses this declaration.
- Complex.continuous_reproof · cited by 60
- IsSelfAdjoint.spectrumRestrictsstatement · cited by 13
- HasDerivAt.real_of_complexproof · cited by 7
- MeasureTheory.ComplexMeasure.reproof · cited by 7
- HasStrictDerivAt.real_of_complexproof · cited by 6
- IsSelfAdjoint.quasispectrumRestrictsstatement · cited by 6
- InnerProductSpace.HarmonicOnNhd.circleAverage_eqproof · cited by 5
- InnerProductSpace.HarmonicOnNhd.exists_analyticOnNhd_ball_re_eqproof · cited by 4
- cfc_real_eq_complexproof · cited by 4
- Complex.uniformContinuous_reproof · cited by 3
- cfcₙ_real_eq_complexproof · cited by 3
- Complex.restrictScalars_toSpanSingleton'statement and proof · cited by 3