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On boundary value problems for some conformally invariant differential operators

Författare och institution:
J. Mollers (-); B. Orsted (-); Genkai Zhang (Institutionen för matematiska vetenskaper, Chalmers/GU)
Publicerad i:
Communications in Partial Differential Equations, 41 ( 4 ) s. 609-643
ISSN:
0360-5302
E-ISSN:
1532-4133
Publikationstyp:
Artikel, refereegranskad vetenskaplig
Publiceringsår:
2016
Språk:
engelska
Fulltextlänk:
Sammanfattning (abstract):
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.
Ämne (baseras på Högskoleverkets indelning av forskningsämnen):
NATURVETENSKAP ->
Matematik
Nyckelord:
Boundary value problem, complementary series, Plancherel formula, Poisson transform, unitary, fractional laplacian, extension problem
Postens nummer:
237508
Posten skapad:
2016-06-09 15:49
Posten ändrad:
2016-06-17 14:53

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