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Sturm-Liouville Operatörleri için Mochizuki-Trooshin Teoremi Üzerine

Year 2019, Volume: 40 Issue: 1, 108 - 116, 22.03.2019

İbrahim Adalar

https://doi.org/10.17776/csj.470328
https://izlik.org/JA92CP74BW

Abstract

Bu makalede,
Sturm-Liouville operatörlerinin ters spektral problemleri ele alınmıştır. Bazı
yeni teklik teoremleri ve Mochizuki-Trooshin teoreminin benzetimleri
ispatlanmıştır.

Keywords

Ters spektral problem Sturm-Liouville denklemi

References

  • [1]. Ambarzumyan, V.A., Uber eine Frage der Eigenwerttheorie, Z. Phys. 53 (1929) 690-695.
  • [2]. Borg, G., Eine umkehrung der Sturm-Liouvillesehen eigenwertaufgabe, Acta Math. 78 (1946) 1-96.
  • [3]. Gelfand, L.M., Levitan, B.M., On the determination of a differential equation from its spectral function, Izv. Akad. Nauk SSR. Ser. Mat. 15 (1951) 309-360 (in Russian), English transl. in Amer. Math. Soc.. Transl. Ser. 2 (1) (1955) 253-304.
  • [4]. Levitan B.M., Sargsjan I.S., Sturm-Liouville and Dirac Operators. Dordrecht: Kluwer; 1991.
  • [5]. Mochizuki, K., Trooshin, I., Inverse problem for interior spectral data of Sturm-Liouville operator, J. Inverse Ill-posed Probl. 9 (2001) 425-433.
  • [6]. Marchenko V., Some questions in the theory of one-dimensional linear differential operators of the second order. I. Tr.Mosk. Mat. Obs. (1952) 1:327-420. (Russian). English transl. in Am.Math. Soc. Trans. (1973) 2:1-104.
  • [7]. Hochstadt, H., Lieberman, B., An inverse Sturm-Liouville problem with mixed given data, SIAM J. Appl. Math. 34 (1978) 676-680.
  • [8]. Freiling, G., Yurko, V.A., Inverse Sturm-Liouville Problems and Their Applications, NOVA Science Publishers, New York, 2001.
  • [9]. Levinson, N., The inverse Sturm-Liouville problem, Math. Tidsskr, 13 (1949), 25- 30.
  • [10]. Rubel, L.A., Necessary and suffcient conditions for Carison's theorem on entire functions, Trans. Amer. Math. Soc. vol. 83 (1956) 417-429.
  • [11]. Boas, R.P., Entire functions, New York, Academic Press, 1954.
  • [12]. Mochizuki, K., Trooshin, I., Inverse problem for interior spectral data of the Dirac operator on a finite interval, Publ. RIMS, Kyoto Univ. 38 (2002) 387-395.
  • [13]. Sat, M., Panakhov, E., A uniqueness theorem for Bessel operator from interior spectral data. Abstr. Appl. Anal., Volume 2013, Article ID 713654, 6 pages.
  • [14]. Ozkan, A.S., Amirov, R. Kh., An interior inverse problem for the impulsive Dirac operator, Tamkang Journal of Mathematics, 42 (2011) 259-263.
  • [15]. Horvath, M., Inverse spectral problems and closed exponential systems, Ann. of Math. 162 (2005) 885-918.
  • [16]. Panakhov, E., Sat, M., Inverse problem for the interior spectral data of the equation of hydrogen atom, Ukrainian Mathematical Journal, 64 (2013), no.11.
  • [17]. Guo, Y., Wei, G., Inverse Sturm-Liouville problems with the potential known on an interior subinterval, Appl. Anal., 94 (5) (2015) 1025-1031.
  • [18]. Gesztesy F., Simon B., Inverse spectral analysis with partial information on the potential. II. The case of discrete spectrum. Trans. Am. Math. Soc. 352 (6) (2000) 2765-2787.
  • [19]. Shieh, C.T., Yurko, V.A., Inverse nodal and inverse spectral problems for discontinuous boundary value problems. J. Math. Anal. Appl. 347 (2008) 266-272.

On Mochizuki-Trooshin Theorem for Sturm-Liouville Operators

Year 2019, Volume: 40 Issue: 1, 108 - 116, 22.03.2019

İbrahim Adalar

https://doi.org/10.17776/csj.470328
https://izlik.org/JA92CP74BW

Abstract

In this paper, the
inverse spectral problems of Sturm-Liouville operators are considered. Some new
uniqueness theorems and analogies of the Mochizuki-Trooshin Theorem are proved.



2010 Mathematics Subject Classification. Primary
34A55, 34B24; Secondary 34L05.

Keywords

Inverse spectral problem Sturm-Liouville equation

References

  • [1]. Ambarzumyan, V.A., Uber eine Frage der Eigenwerttheorie, Z. Phys. 53 (1929) 690-695.
  • [2]. Borg, G., Eine umkehrung der Sturm-Liouvillesehen eigenwertaufgabe, Acta Math. 78 (1946) 1-96.
  • [3]. Gelfand, L.M., Levitan, B.M., On the determination of a differential equation from its spectral function, Izv. Akad. Nauk SSR. Ser. Mat. 15 (1951) 309-360 (in Russian), English transl. in Amer. Math. Soc.. Transl. Ser. 2 (1) (1955) 253-304.
  • [4]. Levitan B.M., Sargsjan I.S., Sturm-Liouville and Dirac Operators. Dordrecht: Kluwer; 1991.
  • [5]. Mochizuki, K., Trooshin, I., Inverse problem for interior spectral data of Sturm-Liouville operator, J. Inverse Ill-posed Probl. 9 (2001) 425-433.
  • [6]. Marchenko V., Some questions in the theory of one-dimensional linear differential operators of the second order. I. Tr.Mosk. Mat. Obs. (1952) 1:327-420. (Russian). English transl. in Am.Math. Soc. Trans. (1973) 2:1-104.
  • [7]. Hochstadt, H., Lieberman, B., An inverse Sturm-Liouville problem with mixed given data, SIAM J. Appl. Math. 34 (1978) 676-680.
  • [8]. Freiling, G., Yurko, V.A., Inverse Sturm-Liouville Problems and Their Applications, NOVA Science Publishers, New York, 2001.
  • [9]. Levinson, N., The inverse Sturm-Liouville problem, Math. Tidsskr, 13 (1949), 25- 30.
  • [10]. Rubel, L.A., Necessary and suffcient conditions for Carison's theorem on entire functions, Trans. Amer. Math. Soc. vol. 83 (1956) 417-429.
  • [11]. Boas, R.P., Entire functions, New York, Academic Press, 1954.
  • [12]. Mochizuki, K., Trooshin, I., Inverse problem for interior spectral data of the Dirac operator on a finite interval, Publ. RIMS, Kyoto Univ. 38 (2002) 387-395.
  • [13]. Sat, M., Panakhov, E., A uniqueness theorem for Bessel operator from interior spectral data. Abstr. Appl. Anal., Volume 2013, Article ID 713654, 6 pages.
  • [14]. Ozkan, A.S., Amirov, R. Kh., An interior inverse problem for the impulsive Dirac operator, Tamkang Journal of Mathematics, 42 (2011) 259-263.
  • [15]. Horvath, M., Inverse spectral problems and closed exponential systems, Ann. of Math. 162 (2005) 885-918.
  • [16]. Panakhov, E., Sat, M., Inverse problem for the interior spectral data of the equation of hydrogen atom, Ukrainian Mathematical Journal, 64 (2013), no.11.
  • [17]. Guo, Y., Wei, G., Inverse Sturm-Liouville problems with the potential known on an interior subinterval, Appl. Anal., 94 (5) (2015) 1025-1031.
  • [18]. Gesztesy F., Simon B., Inverse spectral analysis with partial information on the potential. II. The case of discrete spectrum. Trans. Am. Math. Soc. 352 (6) (2000) 2765-2787.
  • [19]. Shieh, C.T., Yurko, V.A., Inverse nodal and inverse spectral problems for discontinuous boundary value problems. J. Math. Anal. Appl. 347 (2008) 266-272.
There are 19 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

İbrahim Adalar 0000-0002-4224-0972

Submission Date October 14, 2018
Acceptance Date January 2, 2019
Publication Date March 22, 2019
DOI https://doi.org/10.17776/csj.470328
IZ https://izlik.org/JA92CP74BW
Published in Issue Year 2019 Volume: 40 Issue: 1

Cite

APA Adalar, İ. (2019). On Mochizuki-Trooshin Theorem for Sturm-Liouville Operators. Cumhuriyet Science Journal, 40(1), 108-116. https://doi.org/10.17776/csj.470328

Cited By

An Inverse Three Spectra Problem for Parameter-Dependent and Jumps Conformable Sturm–Liouville Operators
Bulletin of the Malaysian Mathematical Sciences Society
https://doi.org/10.1007/s40840-023-01610-2

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