feat(Analysis/Distribution): define canonical maps between Schwartz/test functions, distributions/tempered distributions

[aditya-ramabadran]

Defines these canonical maps: (1) continuous linear map from $\mathcal D$ to $\mathcal S$, and (2) induced (linear) restriction map from $\mathcal S'$ to $\mathcal D'$, as assigned by @ADedecker.

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Put in a separate file since Distribution.lean only imports TestFunction right now and I thought it was cleaner to do in a new bridge file with both the maps. Open to changing this though.

• Made use of [Merged by Bors] - feat(TestFunction): add limitCLM, a variant of mkCLM starting from buncled CLMs on D^n_K #36445 (proved first map locally on fixed support spaces first by local seminorm estimates, then used limitCLM)
• Needed a real to complex bridge TestFunction.ToComplexSchwartzMap since distributions are defined on real-valued test functions but tempered distributions in mathlib are defined on complex-valued Schwartz functions
• Induced map $\mathcal S'(E,F) \to \mathcal D'(Ω,F)$ is $\mathbb C$-linear

The main important defs are ContDiffMapSupportedIn.toSchwartzMapCLM which is the local fixed-support part, then TestFunction.toSchwartzMapCLM (where the continuity uses limitCLM to glue the local continuous linear maps on each $\mathcal D_K$), and TemperedDistribution.toDistributionLM which is the linear map from tempered distributions to ordinary distributions.

Tested with lake env lean Mathlib/Analysis/Distribution/TestFunctionSchwartz.lean

[github-actions]

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[github-actions]

PR summary ea0501174b

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.Analysis.Distribution.TestFunctionSchwartz (new file)	2688

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Declarations diff

+ norm_pow_le_bound_on_compact
+ powNormBound
+ restrictToTestFunctionsCLM
+ restrictToTestFunctionsCLM_apply
+ schwartzSeminorm_le_localSeminorm
+ toComplexSchwartzMapCLM
+ toComplexSchwartzMapCLM_apply
+ toComplexSchwartzMapCLM_real_smul
+ toDistribution
+ toDistributionLM
+ toDistributionLM_apply_apply
+ toDistribution_apply
++ toSchwartzMap
++ toSchwartzMapCLM
++ toSchwartzMapCLM_apply
++ toSchwartzMap_apply

You can run this locally as follows

## summary with just the declaration names:
./scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
./scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh contains some details about this script.

---

No changes to technical debt.

You can run this locally as

./scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

[aditya-ramabadran]

fixed the linter/comment errors, should be good to go