Theory of Bessel potentials. III : potentials on regular manifolds

Adams, Robert, Aronszajn, Nachman, and Hanna, M. S.. "Theory of Bessel potentials. III : potentials on regular manifolds." Annales de l'institut Fourier 19.2 (1969): 279-338. <http://eudml.org/doc/73991>.

@article{Adams1969,
abstract = {In this paper Bessel potentials on $C^\infty $-Riemannian manifolds (open or bordered) are studied. Let $\{\bf M\}$ be an $n$-dimensional manifold, and $\{\bf N\}$ a submanifold of $\{\bf M\}$ of dimension $k$. Sufficient conditions are given for: 1) the restriction to $\{\bf N\}$ of any potential of order $\alpha $ on $\{\bf M\}$ to be a potential of order $\alpha -\{n-k\over 2\}$ on $\{\bf N\}$ ; 2) any potential of order $\alpha -\{n-k\over 2\}$ on $\{\bf N\}$ to be extendable to a potential of order $\alpha $ on $\{\bf M\}$. It is also proved that for a bordered manifold $\{\bf M\}$ the restriction to its interior $\{\bf M\}^i$ is an isometric isomorphism between the spaces of potentials of order $\alpha $ on $\{\bf M\}$ and $\{\bf M\}^i$ respectively.},
author = {Adams, Robert, Aronszajn, Nachman, Hanna, M. S.},
journal = {Annales de l'institut Fourier},
keywords = {Bessel potentials on -Riemannian manifolds},
language = {eng},
number = {2},
pages = {279-338},
publisher = {Association des Annales de l'Institut Fourier},
title = {Theory of Bessel potentials. III : potentials on regular manifolds},
url = {http://eudml.org/doc/73991},
volume = {19},
year = {1969},
}

TY - JOUR
AU - Adams, Robert
AU - Aronszajn, Nachman
AU - Hanna, M. S.
TI - Theory of Bessel potentials. III : potentials on regular manifolds
JO - Annales de l'institut Fourier
PY - 1969
PB - Association des Annales de l'Institut Fourier
VL - 19
IS - 2
SP - 279
EP - 338
AB - In this paper Bessel potentials on $C^\infty $-Riemannian manifolds (open or bordered) are studied. Let ${\bf M}$ be an $n$-dimensional manifold, and ${\bf N}$ a submanifold of ${\bf M}$ of dimension $k$. Sufficient conditions are given for: 1) the restriction to ${\bf N}$ of any potential of order $\alpha $ on ${\bf M}$ to be a potential of order $\alpha -{n-k\over 2}$ on ${\bf N}$ ; 2) any potential of order $\alpha -{n-k\over 2}$ on ${\bf N}$ to be extendable to a potential of order $\alpha $ on ${\bf M}$. It is also proved that for a bordered manifold ${\bf M}$ the restriction to its interior ${\bf M}^i$ is an isometric isomorphism between the spaces of potentials of order $\alpha $ on ${\bf M}$ and ${\bf M}^i$ respectively.
LA - eng
KW - Bessel potentials on -Riemannian manifolds
UR - http://eudml.org/doc/73991
ER -