You are here

Home » Content

Süreksizlik Koşullarına Sahip Sturm-Liouville Operatörleri için Teklik Teoremleri

Uniqueness Theorems for Sturm-Liouville Operators With Discontinuity Conditions

Journal Name:

  • Cumhuriyet Üniversitesi Fen Fakültesi Fen Bilimleri Dergisi

Publication Year:

  • 2011

Key Words:

Keywords (Original Language):

Author NameUniversity of AuthorFaculty of Author
Abstract (2. Language): 
In this study, uniquiness theorems for Sturm-Liouville Operators with discontinuity conditions inside an interval have proved and generalization of V. A. Ambartsumyan theorem has been given under the discontinuity conditions.
Bookmark/Search this post with
Abstract (Original Language): 
Bu çalışmada aralığın iç noktasında süreksizlik koşullarına sahip Sturm-Liouville operatörü için teklik teoremleri ispatlanmıs ve V. A. Ambartsumyan teoreminin süreksizlik kosulları altında genellestirilmesi verilmistir. AMS subject classifications: Primary 34A55, Secondary 34B24, 34L05
FULL TEXT (PDF): 
PDF icon arastrmx_32114_3_pp_52-63.pdf
  • 1
52-63
  • English

REFERENCES

References: 

[I] . V.A. Ambartsumyan, Uber eine Frage der Eigenwerttheorie, Z. Physik 53
(1929), 690-695.
[2]. G.Borg, Eine Umkehrung der Sturm-Liouvilleschen Eigenwertaufgabe. Bes-timnung der Differentialgleichung durch die Eigenwerte, Acta Math. 78 (1945), 1-96. [3]. N. Levinson, 1949, The Inverse Sturm-Liouville Problem, Mat. Tidsskr. B.,
pp. 25-30.
[4]. N. Levinson, 1949, Criteria for the Limit-Point Case for Second-Order Linear Differential Operators, Casopis. Pest. Mat. Fya. 74, 17-20.
[5]. V.A. Marchenko, Some Problems in the Theory of Second-order Differential
Operators, Dokl. Akad., Nauk SSSR. 72 (1950), 457-560.
[6]. M.G. Krein, Solution of the Inverse Sturm-Liouville Problem, Dokl. Akad.,
Nauk SSSR, 76 (1951), 21-24.
[7] A.N. Tikhonov, Uniqueness Theorems for Jeophysics Problems, Dokl. Akad.
Nauk. SSSR, Vol 69, No 4, 1949, 797-800.
[8]. I.M. Gelfand and B. M. Levitan, On the Determination of a Differential Equation by its Spectral Function, Izv. Akad. Nauk. SSSR, Ser. Math. 15 (1951),
309-360.
[9]. M.G. Gasimov and B. M. Levitan, About Sturm-Liouville Differential. Op¬erators., Math. Sborn., 63 (105), No. 3, (1964).
[10]. E. Abdukadyrov, 1967, Computation of the Regularized Trace for a Dirac
System, Vestnik Moskov Univ. Ser. Mat. Mekh., 22, (4), 17-24.
[II] . A. B. Khasanov, 1994, On Eigenvalues of the Dirac Operator Located on the Continuous Spectrum, Theory and Math. Phys. v. 99, No:1, 20-26.
[12]. M. G. Gasymov, 1967, The Inverse Scattering Problem for a System of Dirac Equations of Order 2n, Soviet Physics Dokl. 11, 676-678.
[13]. J. Püoschel and E. Trubowitz, 1987 Inverse Spectral Theory(Pure Appl.
Math. Vol 130)(Orlando, FL:Academic).
[14]. R. Kh. Amirov and V. A. Yurko, On Differential Operators with Singularity and Discontinuity Conditions Inside the Interval. Ukr. Math. Jour., 2001, v. 53,
No11, p. 1443-1458.
[15]. R. Kh Amirov, Direct and Inverse Problems for Differential Operators with Singularity and Discontinuity Conditions Inside the Interval Transactions of NAS Azerbaijan. 2002, v. 22, No1, p. 21-38.
[16]. R. Kh Amirov, On Sturm-Liouville Operators with Discontinuity Condi¬tions Inside an Interval J. Math. Anal. Appl. 317 (2006) 163-176.

Thank you for copying data from http://www.arastirmax.com