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Add odd-dimensional iterated norm Laplacian#1175

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Lemmy00:milikic/odd-dimensional-laplacian-core
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Add odd-dimensional iterated norm Laplacian#1175
Lemmy00 wants to merge 1 commit into
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Lemmy00:milikic/odd-dimensional-laplacian-core

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@Lemmy00

@Lemmy00 Lemmy00 commented Jun 12, 2026

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This builds on the norm-power Laplacian and fundamental-solution API added in the preceding PRs.

It adds the odd-dimensional analytic core in a dedicated module: in dimension 2 * m + 1, the (m + 1)-fold distributional Laplacian of the distribution induced by ‖x‖ is an explicit nonzero scalar multiple of diracDelta ℝ 0.

Main additions:

  • Physlib.SpaceAndTime.Space.Norm.IteratedLaplacian
  • oddNormIteratedLaplacianCoeff and oddNormIteratedLaplacianCoeff_ne_zero
  • iterated_distLaplacian_norm_zpow_odd_eq_smul_diracDelta

Verification run locally:

  • lake build Physlib.SpaceAndTime.Space.Norm Physlib.SpaceAndTime.Space.Norm.IteratedLaplacian
  • ./scripts/lint-style.sh
  • lake exe runPhyslibLinters
  • lake build

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@Lemmy00 Lemmy00 force-pushed the milikic/odd-dimensional-laplacian-core branch 2 times, most recently from 34e158d to 9486f22 Compare June 12, 2026 17:14
(((1 : ℤ) - 2 * (m : ℤ) : ℝ) * (2 * m + 1 : ℝ) *
(volume (α := Space (2 * m + 1))).real (Metric.ball 0 1))

private lemma odd_unit_ball_volume_real_pos (m : ℕ) :

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This should be moved to the general Integrals file.


This file proves an odd-dimensional iterated-Laplacian identity for the distribution induced by
the norm on `Space (2 * m + 1)`.

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Can you write what this corresponds to here.


/-- The scalar factor produced by one nonsingular Laplacian step in dimension `2 * m + 1`,
after `k` previous Laplacian steps. -/
noncomputable def oddNormLaplacianStepCoeff (m k : ℕ) : ℝ :=

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Do we actually need to make this definition?

@jstoobysmith jstoobysmith added the awaiting-author A reviewer has asked the author a question or requested changes label Jun 12, 2026
@Lemmy00 Lemmy00 force-pushed the milikic/odd-dimensional-laplacian-core branch from 9486f22 to 0e55af4 Compare June 13, 2026 11:58
@Lemmy00

Lemmy00 commented Jun 13, 2026

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Thanks, addressed these in 0e55af4f.

  • moved the odd unit-ball volume positivity lemma to Space/Integrals/Basic;
  • expanded the file overview to say this corresponds to the odd-dimensional identity where applying the Laplacian m + 1 times to the norm gives a nonzero constant multiple of δ₀;
  • removed the separate step-coefficient definition and inlined the factor in the product.

I also reran the local targeted builds, full lake build, style script, Lean linters, and git diff --check.

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