feat(CStarAlgebra): x ↦ x ^ p is operator concave for p ∈ [0, 1]

[dupuisf]

This PR shows that x ↦ x ^ p is operator concave (i.e. CFC.nnrpow is concave) on positive elements of a C*-algebra for p ∈ [0, 1].

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[github-actions]

PR summary 54d69dfd22

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation	2744	2746	+2 (+0.07%)
Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Order	2745	2747	+2 (+0.07%)

Import changes for all files

Files	Import difference
3 files Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.ExpLog.Order Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.IntegralRepresentation Mathlib.Analysis.SpecialFunctions.ContinuousFunctionalCalculus.Rpow.Order	2

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Declarations diff

+ concaveOn_cfc_rpowIntegrand₀₁
+ concaveOn_cfcₙ_of_concaveOn_cfc
+ concaveOn_cfcₙ_rpowIntegrand₀₁
+ concaveOn_nnrpow
+ concaveOn_nnrpow_Ioo
+ concaveOn_of_concaveOn_inr_comp
+ concaveOn_rpow
+ concaveOn_sqrt
+ convexOn_cfcₙ_of_convexOn_cfc
+ convexOn_of_convexOn_inr_comp
+ convexOn_ringInverse_algebraMap_add
+ inrHom_injective
+ inr_map_Ici_zero
+ rpowIntegrand₀₁_eq_sub

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.

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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).