An extension problem related to the fractional Branson-Gover operators

Jan Frahm; Bent Ørsted; Genkai Zhang

doi:10.1016/j.jfa.2019.108395

An extension problem related to the fractional Branson-Gover operators

Department of Mathematics

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaper › Journal article › Research › peer-review

193 Downloads (Pure)

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 language	English
Article number	108395
Journal	Journal of Functional Analysis
Volume	278
Issue	5
ISSN	0022-1236
DOIs	https://doi.org/10.1016/j.jfa.2019.108395
Publication status	Published - Mar 2020

Keywords

math.AP
math.RT

Access to Document

10.1016/j.jfa.2019.108395

1904.03073v1Other version, 290 KB

Symmetry Breaking in Mathematics
Frahm, J. (PI), Weiske, C. (Participant), Ditlevsen, J. (Participant), Spilioti, P. (Participant), Bang-Jensen, F. J. (Participant) & Labriet, Q. (Participant)
01/08/2019 → 31/07/2024
Project: Research

Cite this

@article{cb73d0d9a85a4aabbb7ad77fc127d15d,

title = "An extension problem related to the fractional Branson-Gover operators",

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. ",

keywords = "math.AP, math.RT",

author = "Jan Frahm and Bent {\O}rsted and Genkai Zhang",

year = "2020",

month = mar,

doi = "10.1016/j.jfa.2019.108395",

language = "English",

volume = "278",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "5",

}

TY - JOUR

T1 - An extension problem related to the fractional Branson-Gover operators

AU - Frahm, Jan

AU - Ørsted, Bent

AU - Zhang, Genkai

PY - 2020/3

Y1 - 2020/3

N2 - 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.

AB - 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.

KW - math.AP

KW - math.RT

U2 - 10.1016/j.jfa.2019.108395

DO - 10.1016/j.jfa.2019.108395

M3 - Journal article

SN - 0022-1236

VL - 278

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 5

M1 - 108395

ER -

An extension problem related to the fractional Branson-Gover operators

Abstract

Keywords

Access to Document

Fingerprint

Projects

Symmetry Breaking in Mathematics

Cite this