On $m$-sectorial Schrödinger-type operators with singular potentials on manifolds of bounded geometry

@article{Milatovic2004,
abstract = {We consider a Schrödinger-type differential expression $H_V=\nabla ^*\nabla +V$, where $\nabla $ is a $C^\{\infty \}$-bounded Hermitian connection on a Hermitian vector bundle $E$ of bounded geometry over a manifold of bounded geometry $(M,g)$ with metric $g$ and positive $C^\{\infty \}$-bounded measure $d\mu $, and $V$ is a locally integrable section of the bundle of endomorphisms of $E$. We give a sufficient condition for $m$-sectoriality of a realization of $H_V$ in $L^2(E)$. In the proof we use generalized Kato’s inequality as well as a result on the positivity of $u\in L^2(M)$ satisfying the equation $(\Delta _M+b)u=\nu $, where $\Delta _M$ is the scalar Laplacian on $M$, $b>0$ is a constant and $\nu \ge 0$ is a positive distribution on $M$.},
author = {Milatovic, Ognjen},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Schrödinger operator; $m$-sectorial; manifold; bounded geometry; singular potential; Schrödinger operator; -sectorial; manifold; bounded geometry; singular potential},
language = {eng},
number = {1},
pages = {91-100},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On $m$-sectorial Schrödinger-type operators with singular potentials on manifolds of bounded geometry},
url = {http://eudml.org/doc/249343},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Milatovic, Ognjen
TI - On $m$-sectorial Schrödinger-type operators with singular potentials on manifolds of bounded geometry
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 1
SP - 91
EP - 100
AB - We consider a Schrödinger-type differential expression $H_V=\nabla ^*\nabla +V$, where $\nabla $ is a $C^{\infty }$-bounded Hermitian connection on a Hermitian vector bundle $E$ of bounded geometry over a manifold of bounded geometry $(M,g)$ with metric $g$ and positive $C^{\infty }$-bounded measure $d\mu $, and $V$ is a locally integrable section of the bundle of endomorphisms of $E$. We give a sufficient condition for $m$-sectoriality of a realization of $H_V$ in $L^2(E)$. In the proof we use generalized Kato’s inequality as well as a result on the positivity of $u\in L^2(M)$ satisfying the equation $(\Delta _M+b)u=\nu $, where $\Delta _M$ is the scalar Laplacian on $M$, $b>0$ is a constant and $\nu \ge 0$ is a positive distribution on $M$.
LA - eng
KW - Schrödinger operator; $m$-sectorial; manifold; bounded geometry; singular potential; Schrödinger operator; -sectorial; manifold; bounded geometry; singular potential
UR - http://eudml.org/doc/249343
ER -