Theorems · Theorem · complex analysis

Complex.HadamardThreeLines.interpStrip_eq_of_mem_verticalStrip

∀ {E : Type u_1} [inst : NormedAddCommGroup E] (f : ℂ → E),
  ∀ z ∈ Complex.HadamardThreeLines.verticalStrip 0 1,
    Complex.HadamardThreeLines.interpStrip f z =
      ↑(Complex.HadamardThreeLines.sSupNormIm f 0) ^ (1 - z) * ↑(Complex.HadamardThreeLines.sSupNormIm f 1) ^ z

Rewrite for InterpStrip on the open vertical strip.

Defined in: Mathlib.Analysis.Complex.Hadamard
Cited by: 1 results in Mathlib
Foundations: Depth 193 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup

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Cites15

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Setstatement · cited by 53,352
Realstatement · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
Complexstatement and proof · cited by 5,565
Complex.ofRealstatement and proof · cited by 1,654
Complex.improof · cited by 591
sub_eq_zeroproof · cited by 407
lt_of_le_of_neproof · cited by 230
ne_of_ltproof · cited by 203
Complex.HadamardThreeLines.sSupNormImstatement and proof · cited by 19
Complex.HadamardThreeLines.verticalStripstatement and proof · cited by 13
Complex.HadamardThreeLines.interpStripstatement · cited by 9

Cited by1

Results whose statement or proof uses this declaration.

Complex.HadamardThreeLines.norm_le_interpStrip_of_mem_verticalStrip_zeroproof · cited by 1