Regular and pathological eigenvalue behavior for the equation -λu″= Vu on the semiaxis

K. Naimark; M. Solomyak

doi:10.1006/jfan.1997.3149

Regular and pathological eigenvalue behavior for the equation -λu″= Vu on the semiaxis

K. Naimark^*
, M. Solomyak

^*Corresponding author for this work

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

25 Scopus citations

Abstract

We study the behavior of the eigenvalue distribution functionn(λ) for the equation-λu″=Vuon R₊,u(0)=0.Typically,n(λ)=O(λ^-1/2) and, moreover,λ^1/2n(λ)→π^-1∫Vdxasλ→0. We obtain criteria for each of these relations. Examples are presented where lim_λ→0λ^1/2n(λ) does exist, but is not equal toπ^-1∫Vdx.

Original language	English
Pages (from-to)	504-530
Number of pages	27
Journal	Journal of Functional Analysis
Volume	151
Issue number	2
DOIs	https://doi.org/10.1006/jfan.1997.3149
State	Published - 15 Dec 1997
Externally published	Yes

Access to Document

10.1006/jfan.1997.3149

Cite this

@article{da4cd97baf6d49c7bf9c0a401e37db96,

title = "Regular and pathological eigenvalue behavior for the equation -λu″= Vu on the semiaxis",

abstract = "We study the behavior of the eigenvalue distribution functionn(λ) for the equation-λu″=Vuon R+,u(0)=0.Typically,n(λ)=O(λ-1/2) and, moreover,λ1/2n(λ)→π-1∫Vdxasλ→0. We obtain criteria for each of these relations. Examples are presented where limλ→0λ1/2n(λ) does exist, but is not equal toπ-1∫Vdx.",

author = "K. Naimark and M. Solomyak",

year = "1997",

month = dec,

day = "15",

doi = "10.1006/jfan.1997.3149",

language = "אנגלית",

volume = "151",

pages = "504--530",

journal = "Journal of Functional Analysis",

issn = "0022-1236",

publisher = "Academic Press Inc.",

number = "2",

}

TY - JOUR

T1 - Regular and pathological eigenvalue behavior for the equation -λu″= Vu on the semiaxis

AU - Naimark, K.

AU - Solomyak, M.

PY - 1997/12/15

Y1 - 1997/12/15

N2 - We study the behavior of the eigenvalue distribution functionn(λ) for the equation-λu″=Vuon R+,u(0)=0.Typically,n(λ)=O(λ-1/2) and, moreover,λ1/2n(λ)→π-1∫Vdxasλ→0. We obtain criteria for each of these relations. Examples are presented where limλ→0λ1/2n(λ) does exist, but is not equal toπ-1∫Vdx.

AB - We study the behavior of the eigenvalue distribution functionn(λ) for the equation-λu″=Vuon R+,u(0)=0.Typically,n(λ)=O(λ-1/2) and, moreover,λ1/2n(λ)→π-1∫Vdxasλ→0. We obtain criteria for each of these relations. Examples are presented where limλ→0λ1/2n(λ) does exist, but is not equal toπ-1∫Vdx.

UR - https://www.scopus.com/pages/publications/0031574605

U2 - 10.1006/jfan.1997.3149

DO - 10.1006/jfan.1997.3149

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:0031574605

SN - 0022-1236

VL - 151

SP - 504

EP - 530

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 2

ER -

Regular and pathological eigenvalue behavior for the equation -λu″= Vu on the semiaxis

Abstract

Access to Document

Other files and links

Fingerprint

Cite this