Theorems · Theorem · complex analysis
Complex.HadamardThreeLines.F_edge_le_one
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] (f : ℂ → E),
∀ ε > 0,
∀ (z : ℂ),
BddAbove (norm ∘ f '' Complex.HadamardThreeLines.verticalClosedStrip 0 1) →
z ∈ Complex.re ⁻¹' {0, 1} → ‖Complex.HadamardThreeLines.F f ε z‖ ≤ 1Proof that F is bounded by one on the edges.
- Defined in
- Mathlib.Analysis.Complex.Hadamard
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
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- 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.preimagestatement and proof · cited by 4,946
- mul_oneproof · cited by 3,885
- one_mulproof · cited by 2,841
- Set.Iccproof · cited by 1,702
- le_of_ltproof · cited by 1,175
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