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[Merged by Bors] - feat: Fourier inversion formula #10810

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@sgouezel sgouezel commented Feb 21, 2024

We show the Fourier inversion formula on finite-dimensional real inner product spaces: if f and its Fourier transform are both integrable, then 𝓕⁻ (𝓕 f) = f at continuity points of f.


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@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. label Feb 21, 2024
@sgouezel sgouezel added the WIP Work in progress label Feb 21, 2024
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot removed the merge-conflict The PR has a merge conflict with master, and needs manual merging. label Feb 21, 2024
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added the blocked-by-other-PR This PR depends on another PR which is still in the queue. label Feb 21, 2024
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added merge-conflict The PR has a merge conflict with master, and needs manual merging. and removed blocked-by-other-PR This PR depends on another PR which is still in the queue. labels Feb 28, 2024
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added blocked-by-other-PR This PR depends on another PR which is still in the queue. and removed merge-conflict The PR has a merge conflict with master, and needs manual merging. blocked-by-other-PR This PR depends on another PR which is still in the queue. labels Feb 28, 2024
@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added the merge-conflict The PR has a merge conflict with master, and needs manual merging. label Mar 4, 2024
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@sgouezel sgouezel added awaiting-review The author would like community review of the PR t-analysis Analysis (normed *, calculus) and removed WIP Work in progress labels Mar 5, 2024
@@ -532,8 +532,10 @@ Measures and integral calculus:
Dirichlet theorem: ''
Fejer theorem: ''
Parseval theorem: 'tsum_sq_fourierCoeff'
Fourier transforms on $\mathrm{L}^1(\R^d)$ and $\mathrm{L}^2(\R^d)$: ''
Fourier transform on $\mathrm{L}^1(\R^d)$: 'Real.fourierIntegral'
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I'm not sure we're supposed to add entries to this file... because it's meant to correspond 1-to-1 to the aggregation list.
cc @PatrickMassot

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Splitting an entry is definitely fine.

Mathlib/Analysis/Fourier/Inversion.lean Outdated Show resolved Hide resolved
Mathlib/Analysis/Fourier/Inversion.lean Outdated Show resolved Hide resolved
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Plancherel’s theorem: ''
Fourier inversion formula: 'Continuous.fourier_inversion'
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And this is also fine.

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Thanks πŸŽ‰

bors merge

@leanprover-community-mathlib4-bot leanprover-community-mathlib4-bot added ready-to-merge This PR has been sent to bors. and removed awaiting-review The author would like community review of the PR labels Mar 5, 2024
mathlib-bors bot pushed a commit that referenced this pull request Mar 5, 2024
We show the Fourier inversion formula on finite-dimensional real inner product spaces: if `f` and its Fourier transform are both integrable, then `𝓕⁻ (𝓕 f) = f` at continuity points of `f`.
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Build failed (retrying...):

mathlib-bors bot pushed a commit that referenced this pull request Mar 5, 2024
We show the Fourier inversion formula on finite-dimensional real inner product spaces: if `f` and its Fourier transform are both integrable, then `𝓕⁻ (𝓕 f) = f` at continuity points of `f`.
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Pull request successfully merged into master.

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@mathlib-bors mathlib-bors bot changed the title feat: Fourier inversion formula [Merged by Bors] - feat: Fourier inversion formula Mar 5, 2024
@mathlib-bors mathlib-bors bot closed this Mar 5, 2024
@mathlib-bors mathlib-bors bot deleted the SG_fourier_inv branch March 5, 2024 16:46
kbuzzard pushed a commit that referenced this pull request Mar 12, 2024
We show the Fourier inversion formula on finite-dimensional real inner product spaces: if `f` and its Fourier transform are both integrable, then `𝓕⁻ (𝓕 f) = f` at continuity points of `f`.
dagurtomas pushed a commit that referenced this pull request Mar 22, 2024
We show the Fourier inversion formula on finite-dimensional real inner product spaces: if `f` and its Fourier transform are both integrable, then `𝓕⁻ (𝓕 f) = f` at continuity points of `f`.
utensil pushed a commit that referenced this pull request Mar 26, 2024
We show the Fourier inversion formula on finite-dimensional real inner product spaces: if `f` and its Fourier transform are both integrable, then `𝓕⁻ (𝓕 f) = f` at continuity points of `f`.
Louddy pushed a commit that referenced this pull request Apr 15, 2024
We show the Fourier inversion formula on finite-dimensional real inner product spaces: if `f` and its Fourier transform are both integrable, then `𝓕⁻ (𝓕 f) = f` at continuity points of `f`.
callesonne pushed a commit that referenced this pull request Apr 22, 2024
We show the Fourier inversion formula on finite-dimensional real inner product spaces: if `f` and its Fourier transform are both integrable, then `𝓕⁻ (𝓕 f) = f` at continuity points of `f`.
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4 participants