An extension problem related to the fractional Branson-Gover operators

Jan Frahm, Bent Ørsted, Genkai Zhang

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Abstract

The Branson-Gover operators are conformally invariant differential operators of even degree acting on differential forms. They can be interpolated by a holomorphic family of conformally invariant integral operators called fractional Branson-Gover operators. For Euclidean spaces we show that the fractional Branson-Gover operators can be obtained as Dirichlet-to-Neumann operators of certain conformally invariant boundary value problems, generalizing the work of Caffarelli-Silvestre for the fractional Laplacians to differential forms. The relevant boundary value problems are studied in detail and we find appropriate Sobolev type spaces in which there exist unique solutions and obtain the explicit integral kernels of the solution operators as well as some of its properties.
Original languageEnglish
Article number108395
JournalJournal of Functional Analysis
Volume278
Issue5
ISSN0022-1236
DOIs
Publication statusPublished - Mar 2020

Keywords

  • math.AP
  • math.RT

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  • Symmetry Breaking in Mathematics

    Frahm, J., Weiske, C., Ditlevsen, J., Spilioti, P., Bang-Jensen, F. J. & Labriet, Q.

    01/08/201931/07/2024

    Project: Research

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