Inverse problems for Sturm–Liouville operators on a star-shaped graph with mixed spectral data

References

• Freiling G, Yurko V. Inverse Sturm–Liouville problems and their applications. Huntington, NY: Nova Science Publishers; 2001.
   Google Scholar
• Marchenko VA. Sturm–Liouville operators and their applications. Naukova Dumka Kiev (1977) (Russian); English transl., Birkhauser (1986).
   Google Scholar
• Rundell W, Sacks PE. The reconstruction of Sturm–Liouville operators. Inverse Probl. 1992;8:457–482. doi: 10.1088/0266-5611/8/3/007
   Web of Science ®Google Scholar
• Exner P, Keating JP, Kuchment P, et al. Analysis on graphs and its applications. Volume 77 of Proc. Sympos. Pure Math. Providence (RI): American Mathematical Society; 2008.
   Google Scholar
• Kuchment P. Graph models of wave propagation in thin structures. Waves Random Media. 2002;12:R1–R24. doi: 10.1088/0959-7174/12/4/201
   Web of Science ®Google Scholar
• Montrol E. Quantum theory on a network. J Math Phys. 1970;11:635–648. doi: 10.1063/1.1665178
   Web of Science ®Google Scholar
• Belishev MI. Boundary spectral inverse problem on a class of graphs (trees) by the BC-method. Inverse Probl. 2004;20:647–672. doi: 10.1088/0266-5611/20/3/002
   Web of Science ®Google Scholar
• Bondarenko NP. Partial inverse problems for the Sturm–Liouville operator on a star-shaped graph with mixed boundary conditions. J Inverse Ill-Posed Probl. 2018;26:1–12. doi: 10.1515/jiip-2017-0001
   Web of Science ®Google Scholar
• Bondarenko NP. A partial inverse problem for the differential pencil on a star-shaped graph. Results Math. 2017;72(4):1933–1942. doi: 10.1007/s00025-017-0683-7
   Web of Science ®Google Scholar
• Bondarenko NP, Shieh C-T. Partial inverse problems for Sturm–Liouville operators on trees. Proc R Soc Edinb Sec A Math. 2017;147:917–933. doi: 10.1017/S0308210516000482
   Web of Science ®Google Scholar
• Bondarenko NP. A partial inverse problem for the Sturm–Liouville operator on a star-shaped graph. Anal Math Phys. 2018;8:155–168. doi: 10.1007/s13324-017-0172-x
   Web of Science ®Google Scholar
• Brown BM, Weikard RA. Borg–Levinson theorem for trees. Proc R Soc Lond Ser A Math Phys Eng Sci. 2005;461:3231–3243. doi: 10.1098/rspa.2005.1513
   Web of Science ®Google Scholar
• Carlson R. Inverse eigenvalue problems on directed graphs. Trans Amer Math Soc. 1999;351:4069–4088. doi: 10.1090/S0002-9947-99-02175-3
   Web of Science ®Google Scholar
• Currie S, Watson BA. Inverse nodal problems for Sturm–Liouville equations on graphs. Inverse Probl. 2007;23:2029–2040. doi: 10.1088/0266-5611/23/5/013
   Web of Science ®Google Scholar
• Kuchment P. Quantum graphs II. Some spectral properties of quantum and combinatorial graphs. J Phys A. 2005;38:4887–4900. doi: 10.1088/0305-4470/38/22/013
   Google Scholar
• Kurasov P, Nowaczyk M. Inverse spectral problem for quantum graphs. J Phys A. 2005;38(22):4901–4915. doi: 10.1088/0305-4470/38/22/014
   Google Scholar
• Law CK, Yanagida E. Solution to an Ambarzumyan problem on trees. Kodai Math J. 2012;35:358–373. doi: 10.2996/kmj/1341401056
   Web of Science ®Google Scholar
• Nizhnik LP. Inverse eigenvalue problems for nonlocal Sturm–Liouville operators on a star graph. Meth Funct Anal Topology. 2012;18:68–78.
   Google Scholar
• Pivovarchik V. Inverse problem for the Sturm–Liouville equation on a simple graph. SIAM J Math Anal. 2000;32:801–819. doi: 10.1137/S0036141000368247
   Web of Science ®Google Scholar
• Yang CF. Inverse spectral problems for the Sturm–Liouville operator on a d-star graph. J Math Anal Appl. 2010;365:742–749. doi: 10.1016/j.jmaa.2009.12.016
   Web of Science ®Google Scholar
• Yang CF, Yang XP. Uniqueness theorems from partial information of the potential on a graph. J Inverse Ill-Posed Prob. 2011;19:631–639.
   Web of Science ®Google Scholar
• Yurko VA. Inverse spectral problems for Sturm–Liouville operators on graphs. Inverse Probl. 2005;21:1075–1086. doi: 10.1088/0266-5611/21/3/017
   Web of Science ®Google Scholar
• Yurko VA. Inverse nodal problems for the Sturm–Liouville differential operators on a star-type graph. Siberian Math J. 2009;50(2):373–378. doi: 10.1007/s11202-009-0043-2
   Web of Science ®Google Scholar
• Yurko VA. Inverse problems for Sturm–Liouville operators on bush-type graphs. Inverse Probl. 2009;25:105008. doi: 10.1088/0266-5611/25/10/105008
   Web of Science ®Google Scholar
• Yurko VA. Inverse spectral problems for differential operators on a graph with a rooted cycle. Tamkang J Math. 2009;40(2):271–286.
   Google Scholar
• Borg G. Eine Umkehrung der Sturm–Liouvilleschen Eigenwertaufgabe. Acta Math. 1946;78:1–96. doi: 10.1007/BF02421600
   Web of Science ®Google Scholar
• Gesztesy F, Simon B. Inverse spectral analysis with partial information on the potential II: the case of discrete spectrum. Trans Amer Math Soc. 2000;352:2765–2787. doi: 10.1090/S0002-9947-99-02544-1
   Web of Science ®Google Scholar
• Hochstadt H, Lieberman B. An inverse Sturm–Liouville problem with mixed given data. SIAM J Appl Math. 1978;34:676–680. doi: 10.1137/0134054
   Web of Science ®Google Scholar
• Horvath M. On the inverse spectral theory of Schrödinger and Dirac operators. Trans Amer Math Soc. 2001;353:4155–4171. doi: 10.1090/S0002-9947-01-02765-9
   Web of Science ®Google Scholar
• Koyunbakan H, Panakhov ES. Half-inverse problem for diffusion operators on the finite interval. J Math Anal Appl. 2007;326:1024–1030. doi: 10.1016/j.jmaa.2006.03.068
   Web of Science ®Google Scholar
• Wang YP. Inverse problems for discontinuous Sturm–Liouville operators with mixed spectral data. Inverse Probl Sci Eng. 2015;23:1180–1198. doi: 10.1080/17415977.2014.981748
   Web of Science ®Google Scholar
• Wang YP, Shieh C-T, Ma YT. Inverse spectral problems for Sturm–Liouville operators with partial information. Appl Math Lett. 2013;26(4):452–456. doi: 10.1016/j.aml.2012.11.007
   Google Scholar
• Wang YP. Inverse problems for a class of Sturm–Liouville operators with the mixed spectral data. Oper Matrices. 2017;11(1):89–99. doi: 10.7153/oam-11-06
   Web of Science ®Google Scholar
• Wei G, Xu HK. Inverse spectral analysis for the transmission eigenvalue problem. Inverse Probl. 2013;29:2561–2586. doi: 10.1088/0266-5611/29/11/115012
   Web of Science ®Google Scholar
• Levinson N. Gap and density theorems. New York: AMS Coll. Publ.; 1940.
   Google Scholar
• Levin BJa. Distribution of zeros of entire functions. Moscow: GITTL; 1956. (in Russian).
   Google Scholar