Theorems · Theorem · complex analysis
Complex.HadamardThreeLines.sSupNormIm_nonneg
∀ {E : Type u_1} [inst : NormedAddCommGroup E] (f : ℂ → E) (x : ℝ), 0 ≤ Complex.HadamardThreeLines.sSupNormIm f xsSup of norm is nonneg applied to the image of f on the vertical line re z = x
- Defined in
- Mathlib.Analysis.Complex.Hadamard
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 119 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.
Cites9
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
- Set.imageproof · cited by 5,609
- Complexstatement and proof · cited by 5,565
- Norm.normproof · cited by 5,413
- Set.preimageproof · cited by 4,946
- Complex.reproof · cited by 882
- Complex.HadamardThreeLines.sSupNormImstatement · cited by 19
- Real.sSup_nonnegproof · cited by 4
Cited by5
Results whose statement or proof uses this declaration.
- Complex.HadamardThreeLines.sSupNormIm_eps_posproof · cited by 6
- Complex.HadamardThreeLines.norm_le_interpStrip_of_mem_verticalStrip_zeroproof · cited by 1
- Complex.HadamardThreeLines.diffContOnCl_interpStripproof · cited by 1
- Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip₀₁'proof · cited by 1
- Complex.HadamardThreeLines.interpStrip_eq_of_mem_verticalStripproof · cited by 1