Theorems · Definition · integral transforms
mellin
{E : Type u_1} → [inst : NormedAddCommGroup E] → [NormedSpace ℂ E] → (ℝ → E) → ℂ → EThe Mellin transform of a function f (for a complex exponent s), defined as the integral of
t ^ (s - 1) • f over Ioi 0.
- Defined in
- Mathlib.Analysis.MellinTransform
- Cited by
- 33 results in Mathlib
- Foundations
- Depth 250 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- MeasureTheory.integralproof · cited by 1,779
- Complex.ofRealproof · cited by 1,654
- MeasureTheory.Measure.restrictproof · cited by 1,646
- Set.Ioiproof · cited by 1,463
- MeasureTheory.MeasureSpace.volumeproof · cited by 1,323
Cited by35
Results whose statement or proof uses this declaration.
- WeakFEPair.Λ₀proof · cited by 13
- HasMellinproof · cited by 7
- IsStrongFEPair.Λ_eqstatement · cited by 6
- mellin_div_conststatement · cited by 4
- WeakFEPair.hasMellinproof · cited by 3
- hasSum_mellin_pi_mul_sqstatement and proof · cited by 3
- mellin_hasDerivAt_of_isBigO_rpowstatement · cited by 2
- HurwitzZeta.hasSum_int_completedCosZetaproof · cited by 2
- IsStrongFEPair.symm_Λ_eqstatement · cited by 2
- hasSum_mellin_pi_mul_sq'statement and proof · cited by 2
- Complex.hasDerivAt_GammaIntegralproof · cited by 1
- mellin_comp_mul_leftstatement · cited by 1