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Theorems · Definition · complex analysis

Complex.imCLM

ℂ →L[ℝ] ℝ

Continuous linear map version of the imaginary part function, from ℂ to ℝ.

Defined in
Mathlib.Analysis.Complex.Basic
Cited by
17 results in Mathlib
Foundations
Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Complex.continuous_im · cited by 32Complex.continuous_imMeasureTheory.ComplexMeasure.im · cited by 7ComplexMeasure.imComplex.uniformContinuous_im · cited by 3Complex.uniformContinuous…Complex.restrictScalars_toSpanSingleton' · cited by 3Complex.restrictScalars_t…Complex.imCLM_norm · cited by 2Complex.imCLM_normAnalyticOnNhd.im_ofReal · cited by 0AnalyticOnNhd.im_ofRealComplex.imCLM_apply · cited by 0Complex.imCLM_applyComplex.imCLM_coe · cited by 0Complex.imCLM_coeComplex.imCLM_enorm · cited by 0Complex.imCLM_enormComplex.imCLM_nnnorm · cited by 0Complex.imCLM_nnnormComplex.differentiable_im · cited by 0Complex.differentiable_imAnalyticAt.im_ofReal · cited by 0AnalyticAt.im_ofRealAnalyticAt.harmonicAt_im · cited by 0AnalyticAt.harmonicAt_imHasDerivWithinAt.complexToReal_fderiv' · cited by 0HasDerivWithinAt.complexT…AnalyticOn.im_ofReal · cited by 0AnalyticOn.im_ofRealReal · cited by 25697RealRingHom.id · cited by 18349RingHom.idComplex · cited by 5565ComplexContinuousLinearMap · cited by 5352ContinuousLinearMapLinearMap.mkContinuous · cited by 9LinearMap.mkContinuousComplex.imLm · cited by 6Complex.imLmComplex.imCLMCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by18

Results whose statement or proof uses this declaration.