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Theorems · Theorem · complex analysis

Function.Periodic.boundedAtFilter_cuspFunction

∀ {h : ℝ} {f : ℂ → ℂ},
  0 < h →
    (Filter.comap Complex.im Filter.atTop).BoundedAtFilter f →
      (nhdsWithin 0 {0}ᶜ).BoundedAtFilter (Function.Periodic.cuspFunction h f)
Defined in
Mathlib.Analysis.Complex.Periodic
Cited by
1 results in Mathlib
Foundations
Depth 192 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.

Function.Periodic.differentiableAt_cuspFunction_zero · cited by 3Periodic.differentiableAt…Set · cited by 53352SetReal · cited by 25697RealComplex · cited by 5565ComplexCompl.compl · cited by 2925Compl.complFilter.atTop · cited by 2405Filter.atTopnhdsWithin · cited by 1912nhdsWithinComplex.im · cited by 591Complex.imFilter.comap · cited by 546Filter.comapAsymptotics.IsBigO.comp_tendsto · cited by 33IsBigO.comp_tendstoFunction.Periodic.invQParam · cited by 18Periodic.invQParamFunction.Periodic.cuspFunction · cited by 18Periodic.cuspFunctioneventually_nhdsWithin_of_forall · cited by 18eventually_nhdsWithin_of_…Asymptotics.IsBigO.congr' · cited by 16IsBigO.congr'Filter.BoundedAtFilter · cited by 14Filter.BoundedAtFilterFunction.Periodic.cuspFunction_eq_of_nonzero · cited by 4Periodic.cuspFunction_eq_…Periodic.boundedAtFilter_cusp…CITED BYCITES

Cites16

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Cited by1

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