Theorems · Theorem · complex analysis
Complex.HadamardThreeLines.norm_invInterpStrip
∀ {E : Type u_1} [inst : NormedAddCommGroup E] (f : ℂ → E) (z : ℂ) {ε : ℝ},
ε > 0 →
‖Complex.HadamardThreeLines.invInterpStrip f z ε‖ =
(ε + Complex.HadamardThreeLines.sSupNormIm f 0) ^ (z.re - 1) *
(ε + Complex.HadamardThreeLines.sSupNormIm f 1) ^ (-z.re)Useful rewrite for the absolute value of invInterpStrip
- Defined in
- Mathlib.Analysis.Complex.Hadamard
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 197 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.
Cites12
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
- Norm.normstatement and proof · cited by 5,413
- Complex.ofRealproof · cited by 1,654
- Complex.restatement and proof · cited by 882
- norm_mulproof · cited by 171
- Complex.ofReal_addproof · cited by 94
- Complex.norm_cpow_eq_rpow_re_of_posproof · cited by 21
- Complex.HadamardThreeLines.sSupNormImstatement and proof · cited by 19
- Complex.HadamardThreeLines.sSupNormIm_eps_posproof · cited by 6
- Complex.HadamardThreeLines.invInterpStripstatement · cited by 5
Cited by2
Results whose statement or proof uses this declaration.
- Complex.HadamardThreeLines.F_edge_le_oneproof · cited by 1