Theorems · Theorem · complex analysis
Complex.HadamardThreeLines.sSupNormIm_eps_pos
∀ {E : Type u_1} [inst : NormedAddCommGroup E] (f : ℂ → E) {ε : ℝ},
ε > 0 → ∀ (x : ℝ), 0 < ε + Complex.HadamardThreeLines.sSupNormIm f xsSup of norm translated by ε > 0 is positive applied to the image of f on the
vertical line re z = x
- Defined in
- Mathlib.Analysis.Complex.Hadamard
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 120 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- NormedAddCommGroup
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Realstatement and proof · cited by 25,697
- NormedAddCommGroupstatement and proof · cited by 15,752
- Complexstatement and proof · cited by 5,565
- Nat.cast_zeroproof · cited by 1,870
- lt_of_not_geproof · cited by 374
- Complex.HadamardThreeLines.sSupNormImstatement and proof · cited by 19
- Complex.HadamardThreeLines.sSupNormIm_nonnegproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- Complex.HadamardThreeLines.norm_invInterpStripproof · cited by 2
- Complex.HadamardThreeLines.F_BddAboveproof · cited by 1
- Complex.HadamardThreeLines.norm_le_interpStrip_of_mem_verticalStrip_zeroproof · cited by 1
- Complex.HadamardThreeLines.F_edge_le_oneproof · cited by 1
- Complex.HadamardThreeLines.diffContOnCl_invInterpStripproof · cited by 1