An extension problem related to the fractional Branson–Gover operators
Journal article, 2020

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 their properties.

Extension problem

Branson–Gover operators

Differential forms

Poisson transform


Jan Frahm

Aarhus University

Bent Ørsted

Aarhus University

Genkai Zhang

Chalmers, Mathematical Sciences, Analysis and Probability Theory

Journal of Functional Analysis

0022-1236 (ISSN) 1096-0783 (eISSN)

Vol. 278 5 108395

Subject Categories

Computational Mathematics


Mathematical Analysis



More information

Latest update