Map · 42
harmonic analysis
MSC 42 · Harmonic analysis on Euclidean spaces
354 declarations (316 theorems, 38 definitions) across 14 files. 2 of the 5 famous theorems listed for this area are in Mathlib (40%). 13 open conjectures here are stated in Lean.
Files are assigned to areas by a language model reading each file's documentation. Report a file that is in the wrong area.
Subareas2
- 42A Harmonic analysis in one variable 316
- 42B Harmonic analysis in several variables 38
Famous theorems2 of 5
From the 1000+ theorems project, which classifies each theorem by MSC area.
Not yet in Mathlib · 3
In Mathlib · 2
- Parseval's theoremtsum_sq_fourierCoeff
- Plancherel theoremSchwartzMap.integral_inner_fourier_fourier
From the 100 theorems list1
Open conjectures stated in Lean13
Statements without proofs, collected by the Formal Conjectures project.
- Erdos996.erdos_996Erdős Problems
- Green35.green_35.lowerGreen's Open Problems
- Green35.green_35.upperGreen's Open Problems
- Green7.green_7.variants.positive_densityGreen's Open Problems
- Green82.green_82Green's Open Problems
- Kakeya.kakeya_set_conjectureWikipedia
- WeakTiling.problem_4_1Papers
Files14
Largest first. The code after each file is its assigned subarea.
- Mathlib.Analysis.Fourier.AddCircle
Fourier analysis on the additive circle
42A · 70
- Mathlib.Analysis.Fourier.FourierTransform
The Fourier transform
42A · 54
- Mathlib.Analysis.Fourier.FourierTransformDeriv
Derivatives of the Fourier transform
42A · 49
- Mathlib.Analysis.Fourier.AddCircleMulti
Multivariate Fourier series
42B · 38
- Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform
Fourier transform of the Gaussian
42A · 25
- Mathlib.Analysis.Fourier.ZMod
Fourier theory on `ZMod N`
42A · 24
- Mathlib.Analysis.Fourier.BoundedContinuousFunctionChar
Definition of BoundedContinuousFunction.char
42A · 18
- Mathlib.Analysis.Fourier.LpSpace
The Fourier transform on $L^p$
42A · 17
- Mathlib.Analysis.Fourier.Convolution
The Fourier transform of the convolution
42A · 12
- Mathlib.Analysis.Polynomial.Fourier
Fourier Coefficients of Polynomials
42A · 12
- Mathlib.Algebra.BigOperators.Balance
Balancing a function
42A · 10
- Mathlib.Analysis.Fourier.RiemannLebesgueLemma
The Riemann-Lebesgue Lemma
42A · 10