Theorems · Theorem · harmonic analysis

GaussianFourier.integrable_cexp_neg_mul_sq_norm_add_of_euclideanSpace

∀ {b : ℂ} {ι : Type u_2} [inst : Fintype ι],
  0 < b.re →
    ∀ (c : ℂ) (w : EuclideanSpace ℝ ι),
      MeasureTheory.Integrable (fun v => Complex.exp (-b * ↑‖v‖ ^ 2 + c * ↑(inner ℝ w v))) MeasureTheory.volume

Defined in: Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform
Cited by: 1 results in Mathlib
Foundations: Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Fintype

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Realstatement and proof · cited by 25,697
TopologicalSpaceproof · cited by 24,529
MeasurableSpaceproof · cited by 13,106
MeasureTheory.Measureproof · cited by 10,939
ENNRealstatement · cited by 9,879
Fintypestatement and proof · cited by 7,736
Complexstatement and proof · cited by 5,565
Norm.normstatement and proof · cited by 5,413
Finset.sumproof · cited by 5,195
Finset.univproof · cited by 3,473
Finset.sum_congrproof · cited by 2,323
mul_commproof · cited by 2,262

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GaussianFourier.integrable_cexp_neg_mul_sq_norm_addproof · cited by 1