A uniqueness theorem for inverse nodal problem

References

• Ambartsumyan, VA, 1929. Über eine frage der eigenwerttheorie, Zeitschrift für Physik 53 (1929), pp. 690–695.
   Google Scholar
• Browne, PJ, and Sleeman, BD, 1996. Inverse nodal problem for Sturm-Liouville equation with eigenparameter dependent boundary conditions, Inverse Problems 12 (1996), pp. 377–381.
   Web of Science ®Google Scholar
• Carlson, R, 1997. A Borg-Levinson theorem for Bessel operator, Pacific Journal of Mathematics 177 (1) (1997), pp. 1–26.
   Web of Science ®Google Scholar
• Cheng, YH, Law, C-K, and Tsay, J, 2000. Remarks on a new inverse nodal problem, Journal of Mathematical Analysis and Applications 248 (2000), pp. 145–155.
   Web of Science ®Google Scholar
• Chadan, K, Colton, D, Paivarinta, L, and Rundell, W, 1997. An Introduction to Inverse Scattering and Inverse Spectral Problems. Philadelphia: Siam; 1997.
   Google Scholar
• Chadan, K, and Sabatier, P, 1977. Inverse Problems in Quantum Scattering Theory. New York: Springer; 1977.
   Google Scholar
• Feng, X, and Yang, , 1997. A solution of the inverse nodal problem, Inverse Problems 13 (1997), pp. 203–213.
   Web of Science ®Google Scholar
• Freeiling, G, Rykhlov, V, and Yurko, V, 2002. Spectral analysis for an indefinite singular Sturm-Liouville problem, Applicable Analysis 81 (2002), pp. 1283–1305.
   Google Scholar
• Gelfand, IM, and Levitan, BM, 1951. On the determination of a differential equation from its spectral function, Transitions of American Mathematical Society 1 (1951), pp. 253–304.
   Google Scholar
• Gilbert, RP, 1969. A method of ascent for solving boundary value problems, Bulletin of American Mathematical Society 75 (1969), pp. 1286–1289.
   Web of Science ®Google Scholar
• Hald, OH, and McLaughlin, JR, 1989. Solutions of inverse nodal problems, Inverse Problems 5 (1989), pp. 307–347.
   Web of Science ®Google Scholar
• Hald, O, 1984. Discontinuous inverse eigenvalue problem, Communication on Pure and Applied Mathematics 37 (1984), pp. 539–577.
   Web of Science ®Google Scholar
• Hochstadt, H, 1973. The inverse Sturm-Liouville problem, Communication on Pure and Applied Mathematics 26 (1973), pp. 715–729.
   Web of Science ®Google Scholar
• Hochstadt, H, 1971. The Functions of Mathematical Physics. New York: Wiley-Interscience; 1971.
   Google Scholar
• Koyunbakan, H, 2002. "Spectral analysis of Singular Sturm-Liouville operators". In: PhD thesis. University of Firat; 2002.
   Google Scholar
• Koyunbakan, H, and Panakhov, ES, 2003. Transformation operator for singular Sturm-Liouville equations, International Journal of Pure and Applied Mathematics 14 (2) (2003), pp. 135–143.
   Google Scholar
• Krall, MA, 1982. Boundary values for an eigenvalue problem with a singular potential, Journal of Differential Equation 45 (1982), pp. 128–138.
   Web of Science ®Google Scholar
• Levitan, BM, 1978. On the determination of the Sturm-Liouville operator from one and two spectra, Mathematics of the USSR Izvestija 12 (1978), pp. 179–193.
   Web of Science ®Google Scholar
• Levitan, BM, 1987. Inverse Sturm-Liouville Problems. Utrecht: VNU Science Press; 1987.
   Google Scholar
• Levitan, BM, and Sargsjan, IS, 1975. "Translations of Mathematical Monographs". In: Introduction to Spectral Theory: Self-Adjoint Ordinary Differential Operators. Vol. 39. Providence, RI: American Mathematical Society (AMS); 1975.
   Google Scholar
• McLaughlin, JR, 1988. Inverse spectral theory using nodal points as data -- a uniqueness result, Journal of Differential Equations 73 (1988), pp. 354–362.
   Web of Science ®Google Scholar
• Pöschel, J, and Trubowitz, E, 1987. Inverse Spectral Theory. Orlando: Academic Press; 1987.
   Google Scholar
• Rundell, W, and Sack, EP, 2001. Reconstruction of a radially symmetric potential from two spectral sequences, Journal of Mathematical Analysis and Applications 264 (2001), pp. 354–381.
   Web of Science ®Google Scholar
• Isaacson, EL, and Trubowitz, E, 1983. The inverse Sturm-Liouville problem. I, Communication on Pure and Applied Mathematics 36 (1983), pp. 767–783.
   Web of Science ®Google Scholar
• Chen, Ya-Ting, Cheng, YH, Law, CK, and Tsa, J, 2002. Convergence of the reconstruction formula for the potential function, Proceedings of the American Mathematical Society 130 (2002), pp. 2319–2324.
   Web of Science ®Google Scholar