Theorems · Theorem · complex analysis
Complex.HadamardThreeLines.scale_diffContOnCl
∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℂ E] {f : ℂ → E} {l u : ℝ},
l < u →
DiffContOnCl ℂ f (Complex.HadamardThreeLines.verticalStrip l u) →
DiffContOnCl ℂ (Complex.HadamardThreeLines.scale f l u) (Complex.HadamardThreeLines.verticalStrip 0 1)The function scale f l u is diffContOnCl.
- Defined in
- Mathlib.Analysis.Complex.Hadamard
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- NormedSpacestatement and proof · cited by 12,499
- Complexstatement and proof · cited by 5,565
- Complex.ofRealproof · cited by 1,654
- DiffContOnClstatement and proof · cited by 92
- differentiable_idproof · cited by 35
- Differentiable.diffContOnClproof · cited by 15
- Complex.HadamardThreeLines.verticalStripstatement and proof · cited by 13
- DiffContOnCl.compproof · cited by 10
- Complex.HadamardThreeLines.scalestatement · cited by 9
- DiffContOnCl.smul_constproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- Complex.HadamardThreeLines.norm_le_interp_of_mem_verticalClosedStrip'proof · cited by 0