Theorems · Definition · complex analysis
Complex.HadamardThreeLines.sSupNormIm
{E : Type u_1} → [NormedAddCommGroup E] → (ℂ → E) → ℝ → ℝThe supremum of the norm of f on imaginary lines. (Fixed real part)
This is also known as the function M
- Defined in
- Mathlib.Analysis.Complex.Hadamard
- Cited by
- 19 results in Mathlib
- Foundations
- Depth 113 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.
Cites8
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
- SupSet.sSupproof · cited by 954
- Complex.reproof · cited by 882
Cited by22
Results whose statement or proof uses this declaration.
- Complex.HadamardThreeLines.interpStripproof · cited by 9
- Complex.HadamardThreeLines.sSupNormIm_eps_posstatement and proof · cited by 6
- Complex.HadamardThreeLines.invInterpStripproof · cited by 5
- Complex.HadamardThreeLines.sSupNormIm_nonnegstatement · cited by 5
- Complex.HadamardThreeLines.interpStrip_eq_of_posstatement and proof · cited by 3
- Complex.HadamardThreeLines.interpStrip_eq_of_zerostatement and proof · cited by 3
- Complex.HadamardThreeLines.interpStrip'proof · cited by 2
- Complex.HadamardThreeLines.norm_invInterpStripstatement and proof · cited by 2
- Complex.HadamardThreeLines.F_BddAboveproof · cited by 1
- Complex.HadamardThreeLines.F_edge_le_oneproof · cited by 1
- Complex.HadamardThreeLines.diffContOnCl_interpStripproof · cited by 1
- Complex.HadamardThreeLines.diffContOnCl_invInterpStripproof · cited by 1