The Krein string and characteristic functions of non-self-adjoint operators
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 33, Tome 327 (2005), pp. 115-134 Cet article a éte moissonné depuis la source Math-Net.Ru

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The operator generated by the Krein string is investigated in the framework of the extension theory of symmetric operators. A simple proof of the complete non-self-adjointness of the operator is proposed. The scattering function of the string is obtained with the help of the Derkach–Malamud formula for characteristic functions of almost solvable extensions.
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A. S. Kostenko. The Krein string and characteristic functions of non-self-adjoint operators. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 33, Tome 327 (2005), pp. 115-134. http://geodesic.mathdoc.fr/item/ZNSL_2005_327_a7/

[1] A. A. Adamyan, D. Z. Arov, “Ob unitarnykh stsepleniyakh poluunitarnykh operatorov”, Mat. issledovaniya, 2 (1966), 3–64, Kishinev

[2] D. Z. Arov, “Realizatsiya kanonicheskoi sistemy s dissipativnym kraevym usloviem na odnom kontse segmenta po koeffitsientu dinamicheskoi podatlivosti”, Sib. mat. zhurn., 16:3 (1975), 440–463 | MR | Zbl

[3] D. Z. Arov, A. A. Nudelman, “Passive linear stationary dynamical scattering systems with continuous time”, Integr. Equat. Oper. Theory, 24:1 (1996), 1–45 | DOI | MR | Zbl

[4] M. S. Brodskii, Treugolnye i zhordanovy predstavleniya lineinykh operatorov, Nauka, M., 1969 | MR

[5] V. I. Gorbachuk, M. L. Gorbachuk, Granichnye zadachi dlya differentsialno-operatornykh uravnenii, Naukova dumka, Kiev, 1984 | MR | Zbl

[6] I. Ts. Gokhberg, M. G. Krein, Teoriya volterrovykh operatorov v gilbertovom prostranstve i ee prilozheniya, Nauka, M., 1967 | MR

[7] V. A. Derkach, M. M. Malamud, “Kharakteristicheskie funktsii pochti razreshimykh rasshirenii ermitovykh operatorov”, Ukr. mat. zhurn., 44 (1992), 435–459 | MR | Zbl

[8] V. A. Derkach, M. M. Malamud, Rasshirenie teorii ermitovykh operatorov i problema momentov. Analiz 3, Itogi nauki i tekhniki. Seriya Sovrem. mat. i ee pril., 5, VINITI, M., 1993

[9] I. S. Kats, M. G. Krein, “O spektralnykh funktsiyakh struny”, Dopolnenie II k knige F. Atkinsona, Diskretnye i nepreryvnye zadachi, Mir, M., 1968 | MR

[10] M. G. Krein, A. A. Nudelman, “O nekotorykh spektralnykh svoistvakh neodnorodnoi struny s dissipativnym granichnym usloviem”, J. Operator Theory, 22 (1989), 369–395 | MR | Zbl

[11] M. M. Malamud, S. M. Malamud, “Spektralnaya teoriya operatornykh mer v gilbertovom prostranstve”, Algebra i analiz, 15 (2003), 1–77 | MR | Zbl

[12] M. A. Nudelman, “Struna Kreina i kharakteristicheskie funktsii maksimalnykh dissipativnykh operatorov”, Zap. nauchn. semin. POMI, 290, 2002, 138–167 | MR | Zbl

[13] Yu. L. Shmulyan, Invariantnye podprostranstva polugrupp i skhema Laksa–Fillipsa, Odesskii institut inzhenerov morskogo flota, Odessa Dep. v VINITI 12.11.86, No 8009-V86, 1986

[14] H. Dym, H. P. McCean, Gaussian Processes, Function Theory and the Inverse Spectral Problem, Acad. Press, New York, 1976 | MR | Zbl

[15] S. V. Hruščev, “The Regge problem for strings, unconditionally convergent eigenfunction expansions, and unconditional bases of exponentials in $L^2(-T,T)$”, J. Operator Theory, 14 (1985), 67–85 | MR | Zbl

[16] M. Lesch, M. Malamud, “On the deficiency indices and self-adjontness of symmetric Hamiltonian systems $L^{2}(\mathbb{R})$”, J. Diff. Eqs, 189 (2003), 556–615 | DOI | MR | Zbl