有限区间上的扩散算子的惟一性定理

Abstract

CLC Number:

34A55

WANG Yu-Ping. A Uniqueness Theorem for Diffusion Operators on the Finite Interval[J].Acta mathematica scientia,Series A, 2013, 33(2): 333-339.

Trendmd

References

[1] Ambartsumyan V A. \"{U}ber eine frage der eigenwerttheorie. Zeitschrift f\"{u}r Physik, 1929, 53: 690--695

[2] Borg G. Eine umkehrung der Sturm-Liouvillesehen eigenwertaufgabe. Acta Mathematica, 1945, 78: 1--96

[3] Gesztesy F, Simon B. Inverse spectral analysis with partial information on the potential II: the case of discrete spectrum. Trans Amer Math Soc, 2000, 352(6): 2765--2787

[4] Hald O H. The Sturm-Liouville Problem with symmetric potentials. Acta Math, 1978, 141: 262--291

[5] Levitan B M. On the determination of the Sturm-Liouville operator from one and two spectra. Mathematics of the USSR Izv, 1978, 12}: 179--193

[6] Hochstadt H, Lieberman B. An inverse Sturm-Liouville problem with mixed given data. SIAM Journal of Applied Mathematics, 1978, 34: 676--680

[7] McLaughlin J R, Rundell W. A uniqueness theorem for an inverse Sturm-Liouville problem. Journal of Mathematical Physics, 1987, 28(7): 1471--1472

[8] Koyunbakan H. Inverse spectral problem for some singular differential operators. Tamsui Oxford Journal of Mathematical Sciences, 2009, 25(3): 277--283

[9] Jaulent M, Jean C. The inverse s-wave scattering problem for a class of potentials depending on energy. Comm Math Phys, 1972, 28: 177--220

[10] Gasymov M G, Guseinov G S. Determination of diffusion operators on the spectral data 1. Dokl Akad Nauk Azerb SSR, 1981, 37(2): 19--23

[11] Koyunbakan H, Panakhov E S. Half-inverse problem for diffusion operators on the finite interval. J Math Anal Appl, 2007, 326: 1024--1030

[12] 王於平, 杨传富, 黄振友. Schr\"odinger 算子的二次微分束的半逆问题. 数学物理学报, 2011, 31(6): 1708--1717

[13] Yang C F. Reconstruction of the diffusion operator from nodal data. Z Natureforsch, 2010, 65A: 100--106

[14] Nabiev I M. The inverse quasiperiodic problem for a diffusion operator. Doklady Mathematics, 2007, 76(1): 527--529

[15] Wei G S, Xu H K. On the missing eigenvalue problem for an inverse Sturm-Liouville problem. J Math Pures Appl, 2009, 91: 468--475

[16] Yurko V A. Inverse spectral problems for Sturm-Liouville differential operators on a finite interval. J Inverse and Ill-Posed Problems, 2009, 17: 639--694

[17] 杨传富, 杨孝平. 一般边界条件下Sturm-Liouville 算子的 Ambarzumyan型定理. 数学物理学报, 2010, 30(2): 449--455

[18] Ding X Q, Lou P Z. On Ritz method of an integro-differential equation. Acta Math Scientia, 2009, 29: 687--696

[19] Ding X Q, Lou P Z. Finite element approximatiom of an integro-differential operator. Acta Math Scientia, 2009, 29: 1767--1776

[20] Yurko V A. Method of Spectral Mappings in the Inverse Problem Theory. Utrecht: VSP (Inverse Ill-posed Problems Series), 2002

[21] 刘景麟. 常微分算子谱论. 北京: 科学出版社, 2009

[22] Dunford N, Schwarz J T. Linear Operators (Part II). New York, London: Interscience Publishers, 1963

A Uniqueness Theorem for Diffusion Operators on the Finite Interval

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

[1]	Tan Shenyang, Huang Tiren, Liu Dajin. Estimates for Eigenvalues of the Operator in Divergence Form on H-Type Group [J]. Acta mathematica scientia,Series A, 2018, 38(3): 467-475.
[2]	Wang Shengjun, Han Yazhou. Generalized Picone's Identity and Its Applications for Heisenberg-Greiner Operators [J]. Acta mathematica scientia,Series A, 2017, 37(5): 895-901.
[3]	Luo Hua. Spectral Theory of Linear Weighted Sturm-Liouville Eigenvalue Problems [J]. Acta mathematica scientia,Series A, 2017, 37(3): 427-449.
[4]	Wu Hongxing, Wang Shenghua, Cheng Guofei. The Stability of a Transport Equations Solution with Abstract Boundary Condition in Slab Geometry [J]. Acta mathematica scientia,Series A, 2016, 36(4): 703-714.
[5]	He Yue. New Estimates of Lower Bound for the First Eigenvalue on Compact Manifolds with Positive Ricci Curvature [J]. Acta mathematica scientia,Series A, 2016, 36(2): 215-230.
[6]	Cao Hongzhe, Xu Qingyong. Uniqueness Theorems of Meromorphic Mappings in Several Complex Variables Sharing Few Moving Targets [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1158-1167.
[7]	Li Kun, Zheng Zhaowen. Spectral Properties for Sturm-Liouville Equations with Transmission Conditions [J]. Acta mathematica scientia,Series A, 2015, 35(5): 910-926.
[8]	WANG Hua, Alatanchang, HUANG Jun-Jie. Multiplicity and Completeness of a Class of \|Hamiltonian \|Operators and Its Applications [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1507-1517.
[9]	LI Ding-Wu, LIU Wei, SHEN Jin-Rong, XIONG Hui-Jun. Left and Right Inverse Eigenpairs Problem on Disk of Reflexive Matrices [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1542-1553.
[10]	SUN He-Jun. Inequalities for Lower Order Eigenvalues of the Folland-Stein Operator and Quadratic Polynomial Operator of the Kohn Laplacian [J]. Acta mathematica scientia,Series A, 2014, 34(5): 1133-1143.
[11]	Leszek GASI′ NSKI, Nikolaos S. PAPAGEORGIOU. POSITIVE SOLUTIONS FOR PARAMETRIC EQUIDIFFUSIVE p-LAPLACIAN EQUATIONS [J]. Acta mathematica scientia,Series A, 2014, 34(3): 610-618.
[12]	Wu Shi-Liang, LI Cui-Xia. Spectral Analysis on Some Discrete Systems From Maxwell Equations [J]. Acta mathematica scientia,Series A, 2014, 34(1): 109-114.
[13]	QU Feng-Long, LI Xi-Liang. The Interior Transmission Problem for Isotropic Maxwell Equations and Some Estimates on the Index of Refraction [J]. Acta mathematica scientia,Series A, 2013, 33(6): 1178-1188.
[14]	WANG Yu-Ping. Inverse Problem for Diffusion Operators from Interior Spectral Data [J]. Acta mathematica scientia,Series A, 2013, 33(6): 1189-1195.
[15]	DU Feng, WU Chuan-Xi, LI Guang-Han. Estimates for Eigenvalues of the Elliptic Operator in Divergence Form on the Heisenberg Group [J]. Acta mathematica scientia,Series A, 2012, 32(6): 1032-1040.