A. M. Akhtyamov, V. A. Sadovnichy, Ya. T. Sultanaev, “Generalizations of Borg's uniqueness theorem to the case of nonseparated boundary conditions”, Eurasian Math. J., 2012, Volume 3, Number 4,Pages <nobr>10

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Generalizations of Borg's uniqueness theorem to the case of nonseparated boundary conditions

A. M. Akhtyamov^ab, V. A. Sadovnichy^c, Ya. T. Sultanaev^b

^a Bashkir State University, Ufa, Russia
^b Mavlutov Institute of Mechanics, Russian Academy of Sciences, Ufa, Russia
^c M. V. Lomonosov Moscow State University, Moscow, Russia

Abstract: Inverse Sturm–Liouville problems and generalizations of Borg's uniqueness theorem to the case of general boundary conditions are considered. Chudov, Marchenko, Krein, Karaseva and authors' generalizations are adduced. New generalizations of Borg, Marchenko and Karaseva's uniqueness theorem to the case of nonseparated boundary conditions are obtained. Appropriate examples and counterexample are given.

Keywords and phrases: inverse eigenvalue problem, inverse Sturm–Liouville problem, nonseparated boundary conditions.

MSC: 34A55, 34B05, 58C40

Received: 11.06.2012

Language: English