Theorems · Theorem · complex analysis
Complex.HadamardThreeLines.sSupNormIm_scale_left
∀ {E : Type u_1} [inst : NormedAddCommGroup E] (f : ℂ → E) {l u : ℝ},
l < u →
Complex.HadamardThreeLines.sSupNormIm (Complex.HadamardThreeLines.scale f l u) 0 =
Complex.HadamardThreeLines.sSupNormIm f lThe supremum of the norm of scale f l u on the line z.re = 0 is the same as the supremum
of f on the line z.re = l.
- Defined in
- Mathlib.Analysis.Complex.Hadamard
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 114 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.
Cites32
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- 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
- one_mulproof · cited by 2,841
- add_zeroproof · cited by 2,707
- Set.extproof · cited by 2,266
- MulZeroClass.mul_zeroproof · cited by 2,091
- Nat.cast_zeroproof · cited by 1,870
Cited by1
Results whose statement or proof uses this declaration.
- Complex.HadamardThreeLines.interpStrip_scaleproof · cited by 1