Goloshchapova, N. I.; Oridoroga, L. L. The one-dimensional Schrödinger operator with point \(\delta \) - and \(\delta \) -interactions. (English. Russian original) Zbl 1219.34109 Math. Notes 84, No. 1, 125-129 (2008); translation from Mat. Zametki 84, No. 1, 127-131 (2008). Cited in 5 Documents MSC: 34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) 47E05 General theory of ordinary differential operators Keywords:one-dimensional Schrödinger operator; \(\delta \) function; point \(\delta \)- and \(\delta ^{\prime}\)-interactions; Weyl function; Sobolev space; boundary triple of an operator PDF BibTeX XML Cite \textit{N. I. Goloshchapova} and \textit{L. L. Oridoroga}, Math. Notes 84, No. 1, 125--129 (2008; Zbl 1219.34109); translation from Mat. Zametki 84, No. 1, 127--131 (2008) Full Text: DOI OpenURL References: [1] S. Albeverio, F. Gesztesy, R. Høh-Krohn, and H. Holden, Solvable Models in Quantum Mechanics, in TextsMonogr. Phys. (Springer-Verlag, New York, 1988). · Zbl 0679.46057 [2] S. Albeverio and P. Kurasov, Singular Perturbations of Differential Operators: Solvable Schrödinger-Type Operators, in London Math. Soc. Lecture Note Ser. (Cambridge Univ. Press, Cambridge, 2000), Vol. 271. · Zbl 0945.47015 [3] S. Albeverio and L. Niznik, Ukrain.Mat. Zh. 52(5), 582 (2000) [UkrainianMath. J. 44 52 (5), 664 (2000)]. · Zbl 1037.81532 [4] S. Albeverio and L. Niznik, Lett. Math. Phys. 65(1), 27 (2003). · Zbl 1056.34093 [5] S. Albeverio and L. Niznik, Methods Funct. Anal. Topology 9(4), 273 (2003). [6] D. Buschmann, Eindimensionale Schrödingeroperatoren mit lokalen Punktwechselwirkungen, Diploma thesis (Universität Frankfurt, 1994). [7] F. Gesztezy and W. Kirsch, J. Reine Angew.Math. 362, 28 (1985). [8] L. P. Nizhnik, Funktsional. Anal. i Prilozhen. 37(1), 85 (2003) [Functional Anal. Appl. 37 (1), 72 (2003)]. [9] C. S. Christ and G. Stolz, J.Math. Anal. Appl. 184(3), 491 (1994). · Zbl 0805.34077 [10] V. I. Gorbachuk and M. L. Gorbachuk, Boundary-Value Problems for Operator-Differential Equations (Naukova Dumka, Kiev, 1984) [in Russian]. · Zbl 0567.47041 [11] M. M. Malamud, Ukrain.Mat. Zh. 44(2), 215 (1992) [UkrainianMath. J. 44 (2), 190 (1992)]. · Zbl 0788.60074 [12] V. A. Derkach and M. M. Malamud, J. Funct. Anal. 95(1), 1 (1991). · Zbl 0748.47004 [13] N. I. Akhiezer and I. M. Glazman Theory of Linear Operators in Hilbert Space (Vishcha Shkola, Kharkov, 1978; Pitman Advanced Publishing Program, Boston-London-Melbourne, 1981), Vol. 2. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.