Trace Formula on Transmission Eigenvalues of the Sturm-Liouville Problem

被引：1

作者：

Yang, Chuan-Fu ^{[1
]}

机构：

[1] Nanjing Univ Sci & Technol, Dept Appl Math, Nanjing 210094, Jiangsu, Peoples R China

来源：

ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES | 2012年 / 67卷 / 8-9期

基金：

中国国家自然科学基金;

关键词：

Sturm-Liouville Problem; Transmission Eigenvalues; Trace Formula;

D O I：

10.5560/ZNA.2012-0041

中图分类号：

O64 [物理化学（理论化学）、化学物理学];

学科分类号：

070304 ; 081704 ;

摘要：

In this paper, we consider eigenvalues and traces of a special Sturm-Liouville problem, which originates from an acoustic scattering problem with a spherically symmetric speed of sound. Regularized trace formulae on transmission eigenvalues of the Sturm-Liouville problem are obtained.

引用

页码：429 / 434

页数：6

共 12 条

[1] Large eigenvalues and trace formulas for matrix Sturm-Liouville problems
Carlson, R
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1999, 30 (05) : 949 - 962
[2] Eigenvalue estimates and trace formulas for the matrix Hill's equation
Carlson, R
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 167 (01) : 211 - 244
[3] Clark S., 2000, J DIFF EQS, V167, P211
[4] FAR-FIELD PATTERNS FOR ACOUSTIC-WAVES IN AN INHOMOGENEOUS-MEDIUM
COLTON, D
KIRSCH, A
PAIVARINTA, L
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (06) : 1472 - 1483
[5] Colton D., 1988, Q J MECH APPL MATH, V41, P91
[6] DIKIJ LA, 1957, DOKL AKAD NAUK SSSR+, V116, P12
[7] Gelfand I. M., 1953, Dokl. Akad. Nauk SSSR, V88, P593
[8] ON THE UNIQUENESS OF A SPHERICALLY SYMMETRICAL SPEED OF SOUND FROM TRANSMISSION EIGENVALUES
MCLAUGHLIN, JR
POLYAKOV, PL
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1994, 107 (02) : 351 - 382
[9] Traces of differential operators
Sadovnichii, V. A.
Podol'skii, V. E.
[J]. DIFFERENTIAL EQUATIONS, 2009, 45 (04) : 477 - 493
[10] Sansuc J.-J., 1997, Oper. Theory Adv. Appl., V98, P216

← 1 2 →