陳莉敏

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常型Sturm-Liouville算子特征值的漸近式和跡公式

陳莉敏

（常州工程職業(yè)技術(shù)學(xué)院 基礎(chǔ)部，江蘇 常州 213164）

應(yīng)用迭代法計算了自伴型Sturm-Liouville微分算子特征值的漸近式，據(jù)此給出了算子的一類跡公式，并計算出其正則項和跡量.

Sturm-Liouville算子；特征值；跡公式

1 引言及預(yù)備知識

定理1[3]55自伴邊條件下的特征值都是實的.

2 主要結(jié)果及其證明

[1] ATKNSON F V. Discrete and continuous boundary problems[M]. New York: Academic Press, 1964.

[2]EATHEMATICA S P. On the location of spectral concentration for Sturm-Liouville problems with rapidly decaying potential[J]. Mathematica, 1998, 45: 23-36.

[3]劉景麟. 常微分算子譜論[M]. 北京：科學(xué)出版社，2009.

[4]LEVITAN B M, SARGSJAN I S. Sturm-Liouville and Dirac operators[M]. Dordrecht: Kluwer Academic Publishers, 1991.

An Asymptotic Expression and Trace Formula of Eigenvalues for Sturm-Liouville Operators

CHENLi-min

(Department of Basic Courses, Changzhou Institute of Engineering Technology, Changzhou 213164, China)

The coefficients in asymptotic formulae of eigenvalue for Sturm-Liouville operators with self-adjoined boundary condition are calculated, and on the basis of this, a new trace concept and its expressions are introduced.

Sturm-Liouville operators; eigenvalues; trace formulae

1006-7302（2012）02-0025-04

O175

A

2011-11-08

陳莉敏（1977—），女，江蘇揚州人，講師，碩士，研究方向為微分方程.