Physical realization of Bessel heat evolution #
The heat multiplier commutes with the inverse Bessel weight, so the complete Sobolev heat evolution realizes the original physical L² heat flow.
theorem
CKN.Leray.regularisedBesselHeat_realization
(s t : ℝ)
(hs : 0 ≤ s)
(ht : 0 ≤ t)
(v : BesselPotentialSpace Foundation.Parabolic.L2Vec3 ComplexVec3 s 2)
:
regularisedBesselSobolevToL2 s hs (regularisedBesselHeat s t ht v) = heatSemigroup t ht (regularisedBesselSobolevToL2 s hs v)
Realization of the complete Bessel heat semigroup commutes with the physical Fourier L² heat semigroup.