The asymptotic form of the spectral function in Sturm-Liouville problems with a large potential like -xc (c≤2)

被引：12

作者：

Eastham, MSP ^{[1
]}

机构：

[1] Univ Wales, Dept Comp Sci, Cardiff CF1 3NS, S Glam, Wales

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 1998年 / 128卷

关键词：

D O I：

10.1017/S0308210500027141

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A new formula is given for the spectral function in singular Sturm-Liouville problems where the potential is like -(const.)x(c) (0 < c less than or equal to 2). The formula is used to answer an open question concerning the asymptotic form of the spectral function.

引用

页码：37 / 45

页数：9

共 17 条

[1]

[Anonymous], 1982, RES NOTES MATH

[2]

ATKINSON FV, 1982, LECT NOTES MATH, V964

[3] SPECTRAL ASYMPTOTICS FOR STURM-LIOUVILLE EQUATIONS [J].

BENNEWITZ, C .

PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1989, 59 :294-338

[4] AN EXTENSION OF THE LIOUVILLE-GREEN ASYMPTOTIC FORMULA FOR OSCILLATORY 2ND-ORDER DIFFERENTIAL-EQUATIONS [J].

CASSELL, JS .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1985, 100 :181-190

[5]

EARL A., 1955, THEORY ORDINARY DIFF

[6] The asymptotic nature of spectral functions in Sturm-Liouville problems with continuous spectrum [J].

Eastham, MSP .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 213 (02) :573-582

[7]

EASTHAM MSP, 1989, ASYMPTOTOC SOLUTION, V4

[8]

FULTON CT, 1994, J MATH ANAL APPL, V188, P215

[9] ON SUBORDINACY AND ANALYSIS OF THE SPECTRUM OF ONE-DIMENSIONAL SCHRODINGER-OPERATORS [J].

GILBERT, DJ ;

PEARSON, DB .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1987, 128 (01) :30-56

[10] THE ASYMPTOTIC FORM OF THE SPECTRAL FUNCTIONS ASSOCIATED WITH A CLASS OF STURM-LIOUVILLE EQUATIONS [J].

HARRIS, BJ .

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1985, 100 :343-360

← 1 2 →