Advances in Analysis
Some Improvements of Ambarzumyan’s Theorem
Download PDF (359.4 KB) PP. 121 - 123 Pub. Date: July 1, 2018
Author(s)
- Alp Arslan Kıraç*
Department of Mathematics, Faculty of Arts and Sciences, Pamukkale University, 20070, Denizli, Turkey
Abstract
Keywords
References
[1] Ambarzumian, V.: über eine Frage der Eigenwerttheorie. Zeitschrift für Physik 53, 690–695 (1929)
[2] Borg, G.: Eine umkehrung der Sturm-Liouvilleschen eigenwertaufgabe bestimmung der differentialgleichung durch die eigenwerte. Acta Math. 78, 1–96 (1946)
[3] Cheng, Y.H., Wang, T.E., Wu, C.J.: A note on eigenvalue asymptotics for Hill’s equation. Appl. Math. Lett. 23(9), 1013–1015 (2010)
[4] Chern, H.H., Lawb, C.K., Wang, H.J.: Corrigendum to ?SExtension of Ambarzumyan’s theorem to general boundary conditions. J. Math. Anal. Appl. 309, 764–768 (2005)
[5] Chern, H.H., Shen, C.L.: On the n-dimensional Ambarzumyan’s theorem. Inverse Problems 13(1), 15–18 (1997)
[6] Freiling, G., Yurko, V.A.: Inverse Sturm?ULiouville Problems and Their Applications. NOVA Science Publishers, New York (2001)
[7] Hochstadt, H., Lieberman, B.: An inverse sturm-liouville problem with mixed given data. SIAM J. Appl. Math. 34, 676–680 (1978)
[8] Levitan, B.M., Gasymov, M.G.: Determination of a differential equation by two of its spectra. Usp. Mat. Nauk 19, 3–63 (1964)
[9] K?ra?, A.A.: On the Ambarzumyan’s theorem for the quasi-periodic problem. Analysis and Mathematical Physics, http://dx.doi.org/10.1007/s13324-015-0118-0,, 1–4 (2015)
[10] Veliev, O.A., Duman, M.: The spectral expansion for a nonself-adjoint Hill operator with a locally integrable potential. J. Math. Anal. Appl. 265, 76–90 (2002)
[11] Veliev, O.A., K?ra?, A.A.: On the nonself-adjoint differential operators with the quasiperiodic boundary conditions. International Mathematical Forum 2(35), 1703–1715 (2007)
[12] Yang, C.F., Huang, Z.Y., Yang, X.P.: Ambarzumyan’s theorems for vectorial sturm-liouville systems with coupled boundary conditions. Taiwanese J. Math. 14(4), 1429–1437 (2010)
[13] Yurko, V.A.: On Ambarzumyan-type theorems. Applied Mathematics Letters 26, 506–509 (2013)