Regularized trace of the Sturm-Liouville operator with irregular boundary conditions

Electronic Journal of Differential Equations

Volumn 2009, Issue , 2009, Pages 1-8

  Makin, Alexander ^a  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Eigenvalue problem; Spectrum; Sturm Liouville operator

Indexed keywords

EID: 61449117766     PISSN: None     EISSN: 10726691     Source Type: Journal    
DOI: None     Document Type: Article

References (11)

1. L. A. Dikii. On a formula of Gel'fand-Levitan. Uspekhi Math. Nauk, 8, (1953), 119-123 (in Russian).
2. I. M. Gel'fand and B. M. Levitan. On a simple identity for the characteristic values of a differential operator of the second order. Dokl. Akad. Nauk SSSR, 88, (1953), 593-596 (in Russian).
3. P. Lax. Trace formulas for the Schroedinger operator. Comm. Pure Appl. Math., 47, (1994), 503-512.
4. B. M. Levitan and I. S. Sargsyan. Sturm-Liouville and Dirac Operators. Kluwer, Dordrecht, 1991.
5. V. B. Lidskii and V. A. Sadovnichii. Regularized sums of roots of a class of entire functions. Functional Anal, i Priložen., 1, (1967), 52-59 (in Russian); English transl.: Funct. Anal. Appl., 1, (1967), 133-139.
6. A. S. Makin. On the Basis Property of System of Root Functions of Regular Boundary Value Problems for the Sturm-Liouville operator. Differ. Uravn., 42, (2006), 1645-1656 (in Russian); English transl.: Differ. Equations, 42, (2006), 1717-1728.
7. A. S. Makin. Trace Formulas for the Sturm-Liouville Operator with Regular Boundary Conditions. Dokl. Acad. Nauk, 416, (2007), 308-313 (in Russian); English transl.: Dokl. Math., 76, (2007), 702-707.
8. V. A. Marchenko. Sturm-Liouville Operators and Their Applications. Naukova Dumka, Kiev, 1977 (in Russian); English transl.: Birkhäuser, Basel, 1986.
9. M. A. Naimark. Linear Differential Operators. Ungarn, New York, 1967; Nauka, Moscow, 1969 (in Russian).
10. V. A. Sadovnichii and V. E. Podol'skii. Traces of operators. Uspekhi Mat. Nauk, 61, (2006), 89-156 (in Russian); English, transl.: Russian Math. Surveys, 61, (2006), 885-953.
11. J.-J. Sansuc, V. Tkachenko. Characterization of the periodic and antiperiodic spectra of nonselfadjoint Hill's operators. Oper. Theory Adv. Appl., 98, (1997), 216-224.