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On boundary value problems for some conformally invariant differential operators

J. Mollers ; B. Orsted ; Genkai Zhang (Institutionen för matematiska vetenskaper)
Communications in Partial Differential Equations (0360-5302). Vol. 41 (2016), 4, p. 609-643.
[Artikel, refereegranskad vetenskaplig]

We study boundary value problems for some differential operators on Euclidean space and the Heisenberg group which are invariant under the conformal group of a Euclidean subspace, respectively, Heisenberg subgroup. These operators are shown to be self-adjoint in certain Sobolev type spaces and the related boundary value problems are proven to have unique solutions in these spaces. We further find the corresponding Poisson transforms explicitly in terms of their integral kernels and show that they are isometric between Sobolev spaces and extend to bounded operators between certain L-p-spaces.The conformal invariance of the differential operators allows us to apply unitary representation theory of reductive Lie groups, in particular recently developed methods for restriction problems.

Nyckelord: Boundary value problem, complementary series, Plancherel formula, Poisson transform, unitary, fractional laplacian, extension problem



Denna post skapades 2016-06-09. Senast ändrad 2016-06-17.
CPL Pubid: 237508

 

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Institutionen för matematiska vetenskaperInstitutionen för matematiska vetenskaper (GU)

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Matematik

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