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

Commentationes Mathematicae Universitatis Carolinae (2004)

- Volume: 45, Issue: 1, page 91-100
- ISSN: 0010-2628

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topMilatovic, Ognjen. "On $m$-sectorial Schrödinger-type operators with singular potentials on manifolds of bounded geometry." Commentationes Mathematicae Universitatis Carolinae 45.1 (2004): 91-100. <http://eudml.org/doc/249343>.

@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 -

## References

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