Bounded solutions for the Schrödinger operator on Riemannian manifolds

Seok Woo Kim; Yong Hah Lee

doi:10.4134/BKMS.2007.44.3.507

Bounded solutions for the Schrödinger operator on Riemannian manifolds

Seok Woo Kim, Yong Hah Lee

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

Abstract

Let M be a complete Riemannian manifold and L be a Schrödinger operator on M. We prove that if M has finitely many L-nonparabolic ends, then the space of bounded L-harmonic functions on M has the same dimension as the sum of dimensions of the spaces of bounded L-harmonic functions on each L-nonparabolic end, which vanish at the boundary of the end.

Original language	English
Pages (from-to)	507-516
Number of pages	10
Journal	Bulletin of the Korean Mathematical Society
Volume	44
Issue number	3
DOIs	https://doi.org/10.4134/BKMS.2007.44.3.507
State	Published - Aug 2007

Keywords

End
L-harmonic function
L-massive set
Schrödinger operator

Access to Document

10.4134/BKMS.2007.44.3.507

Cite this

@article{7afe7f76135f47b2a4fdba04934862d2,

title = "Bounded solutions for the Schr{\"o}dinger operator on Riemannian manifolds",

abstract = "Let M be a complete Riemannian manifold and L be a Schr{\"o}dinger operator on M. We prove that if M has finitely many L-nonparabolic ends, then the space of bounded L-harmonic functions on M has the same dimension as the sum of dimensions of the spaces of bounded L-harmonic functions on each L-nonparabolic end, which vanish at the boundary of the end.",

keywords = "End, L-harmonic function, L-massive set, Schr{\"o}dinger operator",

author = "Kim, {Seok Woo} and Lee, {Yong Hah}",

year = "2007",

month = aug,

doi = "10.4134/BKMS.2007.44.3.507",

language = "English",

volume = "44",

pages = "507--516",

journal = "Bulletin of the Korean Mathematical Society",

issn = "1015-8634",

publisher = "Korean Mathematical Society",

number = "3",

}

TY - JOUR

T1 - Bounded solutions for the Schrödinger operator on Riemannian manifolds

AU - Kim, Seok Woo

AU - Lee, Yong Hah

PY - 2007/8

Y1 - 2007/8

N2 - Let M be a complete Riemannian manifold and L be a Schrödinger operator on M. We prove that if M has finitely many L-nonparabolic ends, then the space of bounded L-harmonic functions on M has the same dimension as the sum of dimensions of the spaces of bounded L-harmonic functions on each L-nonparabolic end, which vanish at the boundary of the end.

AB - Let M be a complete Riemannian manifold and L be a Schrödinger operator on M. We prove that if M has finitely many L-nonparabolic ends, then the space of bounded L-harmonic functions on M has the same dimension as the sum of dimensions of the spaces of bounded L-harmonic functions on each L-nonparabolic end, which vanish at the boundary of the end.

KW - End

KW - L-harmonic function

KW - L-massive set

KW - Schrödinger operator

UR - http://www.scopus.com/inward/record.url?scp=34548691249&partnerID=8YFLogxK

U2 - 10.4134/BKMS.2007.44.3.507

DO - 10.4134/BKMS.2007.44.3.507

M3 - Article

AN - SCOPUS:34548691249

SN - 1015-8634

VL - 44

SP - 507

EP - 516

JO - Bulletin of the Korean Mathematical Society

JF - Bulletin of the Korean Mathematical Society

IS - 3

ER -

Bounded solutions for the Schrödinger operator on Riemannian manifolds

Abstract

Keywords

Access to Document

Fingerprint

Cite this