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An extension problem related to the fractional Branson-Gover operators

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An extension problem related to the fractional Branson-Gover operators. / Frahm, Jan; Ørsted, Bent; Zhang, Genkai.

In: Journal of Functional Analysis, Vol. 278, No. 5, 108395, 03.2020.

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Frahm, Jan ; Ørsted, Bent ; Zhang, Genkai. / An extension problem related to the fractional Branson-Gover operators. In: Journal of Functional Analysis. 2020 ; Vol. 278, No. 5.

Bibtex

@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",
number = "5",

}

RIS

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

VL - 278

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

SN - 0022-1236

IS - 5

M1 - 108395

ER -