Add odd-dimensional iterated norm Laplacian#1175
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| (((1 : ℤ) - 2 * (m : ℤ) : ℝ) * (2 * m + 1 : ℝ) * | ||
| (volume (α := Space (2 * m + 1))).real (Metric.ball 0 1)) | ||
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| private lemma odd_unit_ball_volume_real_pos (m : ℕ) : |
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This should be moved to the general Integrals file.
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| 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.
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| /-- 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?
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Thanks, addressed these in
I also reran the local targeted builds, full |
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 ofdiracDelta ℝ 0.Main additions:
Physlib.SpaceAndTime.Space.Norm.IteratedLaplacianoddNormIteratedLaplacianCoeffandoddNormIteratedLaplacianCoeff_ne_zeroiterated_distLaplacian_norm_zpow_odd_eq_smul_diracDeltaVerification run locally:
lake build Physlib.SpaceAndTime.Space.Norm Physlib.SpaceAndTime.Space.Norm.IteratedLaplacian./scripts/lint-style.shlake exe runPhyslibLinterslake build