Geodesic
Analogs of Generalized Resolvents for Relations Generated by a Pair of Differential Operator Expressions One of which Depends on Spectral Parameter in Nonlinear Manner
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013), pp. 496-535.

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For the relations generated by a pair of differential operator expressions one of which depends on the spectral parameter in the Nevanlinna manner we construct the analogs of the generalized resolvents which are integro-differential operators. 
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V. Khrabustovskyi. Analogs of Generalized Resolvents for Relations Generated by a Pair of Differential Operator Expressions One of which Depends on Spectral Parameter in Nonlinear Manner. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 9 (2013), pp. 496-535. http://geodesic.mathdoc.fr/item/JMAG_2013_9_a4/

[1] S. Albeverio, M. Malamud, V. Mogilevskii, “On Titchmarsh–Weyl Functions and Eigenfunction Expansions of First-Order Symmetric Systems”, Integr. Equ. Oper. Theory, 2013 | DOI

[2] Mir, M., 1988 | MR | Zbl

[3] John Wiley and Sons Ltd., Chichester, 1989 | MR | Zbl

[4] Naukova Dumka, Kiev, 1965 | MR | Zbl | Zbl

[5] Naukova Dumka, Kiev, 1978

[6] Math. Notes, 15 (1974), 563–568 | DOI | MR | Zbl

[7] Math. Notes, 24 (1979), 767–773 | DOI | MR | Zbl

[8] V. M. Bruk, “Generalized Resolvents of Symmetric Relations Generated on Semi-Axis by a Differential Expression and a Nonnegative Operator Function”, J. Math. Phys. Anal. Geom., 2:4 (2006), 372–387 | MR | Zbl

[9] V. M. Bruk, “On Linear Relations Generated by a Differential Expression and by a Nevanlinna Operator Function”, J. Math. Phys. Anal. Geom., 7:2 (2011), 115–140 | MR | Zbl

[10] V. M. Bruk, “Invertible Linear Relations Generated by Integral Equation with Nevanlinna Measure”, Izv. Vuz. Math., 2013, no. 2, 16–29 (in Russian) | Zbl

[11] Nauka, M., 1970 | Zbl

[12] V. Derkach, S. Hassi, M. Malamud, H. de Snoo, “Boundary Relations and their Weyl Families”, Trans. Amer. Math. Soc., 358:12 (2006), 5351–5400 | DOI | MR | Zbl

[13] V. Derkach, S. Hassi, M. Malamud, H. de Snoo, “Boundary Relations and Generalized Resolvents of Symmetric Operators”, Russ. J. Math. Phys., 16:1 (2009), 17–60 | DOI | MR | Zbl

[14] V. Derkach, M. Malamud, “Generalized Resolvents and the Boundary Value Problems for Hermitian Operators with Gaps”, J. Funct. Anal., 95:1 (1991), 1–95 | DOI | MR | Zbl

[15] A. Dijksma, H. Langer, H. de Snoo, “Symmetric Sturm–Liouville Operator with Eigenvalue Depending Boundary Conditions”, Canadian Math. Soc. Conference Proceedings, 8 (1987), 87–116 | MR

[16] A. Dijksma, H. de Snoo, “Self-Adjoint Extensions of Symmetric Subspaces”, Pacific J. Math., 54 (1974), 71–100 | DOI | MR | Zbl

[17] N. Dunford, D. Schwartz, Linear Operators, v. II, Spectral Theory. Self-adjoint Operators in Hilbert Space, Mir, M., 1966 (in Russian) | Zbl

[18] Naukova Dumka, Kiev, 1984 | MR | Zbl | Zbl

[19] Mir, M., 1972 | MR | Zbl | Zbl

[20] J. Soviet Math., 48:3 (1990), 345–355 | DOI | MR

[21] V. I. Khrabustovskii, “On the Characteristic Matrix of Weyl–Titchmarsh Type for Differential-Operator Equations with the Spectral Parameter which Contains the Spectral Parameter in Linear or Nevanlinna's Manner”, Mat. Fiz. Anal. Geom., 10:2 (2003), 205–227 | MR | Zbl

[22] V. I. Khrabustovsky, “On the Characteristic Operators and Projections and on the Solutions of Weyl Type of Dissipative and Accumulative Operator Systems. I: General Case”, J. Math. Phys. Anal. Geom., 2:2 (2006), 149–175 ; “II: Abstract Theory”:3, 299–317 ; “III: Separated Boundary Conditions”:4, 449–473 | MR | Zbl | MR | Zbl | MR | Zbl

[23] V. I. Khrabustovskyi, “On the Limit of Regular Dissipative and Self-adjoint Boundary Value Problems with Nonseparated Boundary Conditions when an Interval Streches to the Semiaxis”, J. Math. Phys. Anal. Geom., 5:1 (2009), 54–81 | MR

[24] V. I. Khrabustovskyi, “Expansion in Eigenfunctions of Relations Generated by Pair of Operator Differential Expressions”, Methods Funct. Anal. Topol., 15:2 (2009), 137–151 | MR | Zbl

[25] V. I. Khrabustovskyi, Analogs of Generalized Resolvents and Eigenfunction Expansions of Relations Generated by Pair of Differential Operator Expressions one of Which Depends on Spectral Parameter in Nonlinear Manner, arXiv: 1210.5988

[26] Proc. Roy. Soc. Edinburgh, Sect. A, 74 (1975), 5–40

[27] V. E. Lyantse, O. G. Storozh, Methods of the Theory of Unbounded Operators, Naukova Dumka, Kiev, 1983 (in Russian) | MR

[28] Naukova Dumka, Kiev, 1977 | DOI | MR | Zbl

[29] V. Mogilevskii, “Boundary Relations and Boundary Conditions for General (not Necessarily Definite) Canonical Systems with Possibly Unequal Deficiency Indices”, Math. Nachr., 285:14–15 (2012), 1895–1931 | DOI | MR | Zbl

[30] M. A. Naimark, Linear Differential Operators, Nauka, M., 1969 | MR | Zbl

[31] S. A. Orlov, “Description of the Green Functions of Canonical Differential Systems. I; II”, J. Sov. Math., 52:6 (1990), 3500–3508 ; 5, 3372–3377; Teor. Funkts., Funkts. Anal. Prilozh., 51 (1989), 78–88; 52 (1989), 33–39 | DOI | MR | Zbl | MR

[32] F. S. Rofe-Beketov, “Self-adjoin Extensions of Differential Operators in a Space of Vector-Valued Functions”, Teor. Funkts., Funkts. Anal. Prilozh., 8 (1969), 3–24 | MR | Zbl

[33] F. S. Rofe-Beketov, “Square-Integrable Solutions, Self-adjoint Extensions and Spectrum of Differential Systems”, Diff. Equat., Proc. Int. Conf. (Uppsala, 1977), 1977, 169–178 | MR | Zbl

[34] F. S. Rofe-Beketov, A. M. Khol'kin, Spectral Analysis of Differential Operators. Interplay Beetween Spectral and Oscillatory Properties, World Scientific Monograph Series in Mathematics, 7, New York, 2005 | DOI | MR | Zbl

[35] L. A. Sakhnovich, Spectral Theory of Canonical Differential Systems. Method of Operator Idetities, Oper. Theory Adv. App., 107, Birkhauser Verlag, Basel, 1999 | MR | Zbl

[36] Mir, M., 1972 | MR | Zbl

[37] Amer. Math. Soc. Transl. Ser. 2, 16 (1960), 462–464 | MR