Theorems · Theorem · complex analysis

Complex.HadamardThreeLines.norm_mul_invInterpStrip_le_one_of_mem_verticalClosedStrip

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] (f : ℂ → E) (ε : ℝ),
  0 < ε →
    ∀ (z : ℂ),
      DiffContOnCl ℂ f (Complex.HadamardThreeLines.verticalStrip 0 1) →
        BddAbove (norm ∘ f '' Complex.HadamardThreeLines.verticalClosedStrip 0 1) →
          z ∈ Complex.HadamardThreeLines.verticalClosedStrip 0 1 → ‖Complex.HadamardThreeLines.F f ε z‖ ≤ 1

Defined in: Mathlib.Analysis.Complex.Hadamard
Cited by: 1 results in Mathlib
Foundations: Depth 293 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace

Mathlib docs Source Loogle LeanSearch

Around this declaration

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

Cites48

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

Setstatement · cited by 53,352
Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
NormedSpacestatement and proof · cited by 12,499
Set.imagestatement and proof · cited by 5,609
Complexstatement and proof · cited by 5,565
Norm.normstatement and proof · cited by 5,413
Set.preimageproof · cited by 4,946
mul_oneproof · cited by 3,885
LE.le.transproof · cited by 3,151
one_mulproof · cited by 2,841
Filter.atTopproof · cited by 2,405

Cited by1

Results whose statement or proof uses this declaration.

Complex.HadamardThreeLines.norm_le_interpStrip_of_mem_verticalClosedStrip_epsproof · cited by 1