Geodesic
On $m$-sectorial extensions of sectorial operators
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 13 (2017) no. 3, pp. 205-241 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study maximal sectorial extensions of an arbitrary closed densely defined sectorial operator. In particular, abstract boundary conditions for these extensions are obtained. The results are applied for the parametrization of all $m$-sectorial extensions of a nonnegative symmetric operator in a planar model of two-point interactions. 
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Yury Arlinskiǐ; Andrey Popov. On $m$-sectorial extensions of sectorial operators. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 13 (2017) no. 3, pp. 205-241. http://geodesic.mathdoc.fr/item/JMAG_2017_13_3_a0/

[1] V. Adamyan, “Nonnegative Perturbations of Nonnegative”, Self-adjoint Operators, Methods Funct. Anal. Topology, 13:2 (2007), 103–109 | MR | Zbl

[2] S. Albeverio, F. Gestezy, R. Hoegh-Krohn, H. Holden, Solvable Models in Quantum Mechanics, Springer, New York, 1988 | MR | Zbl

[3] R. Arens, “Operational Calculus of Linear Relations”, Pacific J. Math., 11 (1961), 9–23 | DOI | MR | Zbl

[4] Ukrainian Math. J., 40:1 (1988), 5–10 | DOI | MR | Zbl

[5] Ukrainian Math. J., 48 (1996), 809–827 | DOI | MR | Zbl

[6] Yu.M. Arlinskiĭ, “Extremal Extensions of Sectorial Linear Relations”, Mat. Stud., 7, 1997, 81–96 | MR | Zbl

[7] Yu.M. Arlinskiĭ, “On $m$-Accretive Extensions and Restrictions”, Methods Funct. Anal. Topology, 4 (1998), 1–26 | MR | Zbl

[8] Yu.M. Arlinskiĭ, “On Functions connected with Sectorial Operators and their Extensions”, Integral Equations Operator Theory, 33 (1999), 125–152 | DOI | MR | Zbl

[9] Yu. Arlinskiĭ, “Boundary Triplets and Maximal Accretive Extensions of Sectorial Operators”, Operator Methods for Boundary Value Problems, London Mathematical Society Lecture Note Series, 404, Cambridge University Press, London, 2012, 33–70

[10] Yu. Arlinskiĭ, Yu. Kovalev, E. Tsekanovskiĭ, “Accretive and Sectorial Extensions of Nonnegative Symmetric Operators”, Complex Anal. Oper. Theory, 6:3 (2012), 677–718 | DOI | MR | Zbl

[11] Sb. Math., 204:8 (2013), 1085–1121 | DOI | DOI | MR | Zbl

[12] J. Soviet Math., 49:6 (1990), 1241–1247 | DOI | MR | Zbl

[13] M. Ashbaugh, F. Gesztesy, M. Mitrea, R. Shterenberg, G. Teschl, “A Survey on the Kreĭn–von Neumann Extension, the Corresponding Abstract Buckling Problem, and Weyl-type Spectral Asymptotics for Perturbed Kreĭn Laplacians in Nonsmooth Domains”, Oper. Theory Adv. Appl., 232 (2013), 1–106 | DOI | MR | Zbl

[14] V. Derkach, M. Malamud, “On Weyl Function and Hermitian Operators with Gaps”, Dokl. Akad. Nauk SSSR, 293:5 (1987), 1041–1046 | MR | Zbl

[15] V.A. Derkach, M.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

[16] V.A. Derkach, M.M. Malamud, “The Extension Theory of Hermitian Operators and the Moment Problem”, J. Math. Sci., 73:2 (1995), 141–242 | DOI | MR | Zbl

[17] Ukrainian Math. J., 41:2 (1989), 136–142 | DOI | MR | Zbl

[18] F. Gesztesy, N. Kalton, K. Makarov, E. Tsekanovskiĭ, “Some Aplications of Operator-Valued Herglotz Functions”, Oper. Theory Adv. Appl., 123 (2001), 271–321 | MR | Zbl

[19] N. Goloshchapova, “On the Multi-Dimensional Schrödinger Operators with Point Interactions”, Methods Funct. Anal. Topology, 17 (2011), 126–143 | MR | Zbl

[20] Kluwer Academic Publishers, 1991 | MR | Zbl | Zbl

[21] G. Grubb, “Spectral Asymptotics for the “Soft” Selfadjoint Extension of a Symmetric Elliptic Differential Operator”, J. Operator Theory, 10:1 (1983), 9–20 | MR | Zbl

[22] A. Jeffrey, D. Zwillinger, Table of Integrals, Series, and Products, Elsevier Science, 2007 | MR | Zbl

[23] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin–Heidelberg–New York, 1966 | MR | Zbl

[24] A.N. Kochubei, “Extensions of a Positive Definite Symmetric Operator”, Dokl. Akad. Nauk Ukrain. SSR, Ser. A, 1979, no. 3, 168–171 (Russian) | MR

[25] M.G. Kreĭn, “The Theory of Selfadjoint Extensions of Semibounded Hermitian Transformations and its Applications. I; II”, Mat. Sb., 20 (1947), 431–495 | MR | Zbl

[26] M.G. Kreĭn, H. Langer, “Über die Q-Function eines $\Pi$-Hermiteschen Operators im Raum $\Pi_\kappa$”, Acta Sci. Math. (Szeged), 34 (1973), 191–230 | MR | Zbl

[27] M.G. Kreĭn, H. Langer, “On Defect Subspaces and Generalized Resolvents of Hermitian Operator in the Space $\Pi_\kappa$”, Funkcional. Anal. i Priložen, 5:3 (1971), 54–69 (Russian) | MR

[28] V.E. Lyantse, “On a Boundary Problem for Parabolic Systems of Differential Equations with a Strongly Elliptic Right-Hand Side”, Mat. Sb., 35:2 (1954), 367–368 (Russian) | MR

[29] Ukrainian Math. J., 44 (1992), 1522–1547 | DOI | DOI | MR | MR | Zbl

[30] V.A. Mikhailets, “Solvable and Sectorial Boundary-Value Problems for the Operator Sturm–Liouville Equation”, Ukrain. Mat. Zh., 26 (1974), 450–459 (Russian) | MR

[31] F.W.J. Olver, Nist Handbook of Mathematical Functions, National Institute of Standards, and Technology (U.S.), Cambridge University Press, 2010

[32] R. Phillips, “Dissipative Operators and Hyperbolic System of Partial Differential Equations”, Trans. Amer. Math. Soc., 90 (1959), 192–254 | DOI | MR

[33] R.S. Phillips, “On Dissipative Operators”, Lectures in Differential Equations, 3 (1969), 65–113

[34] J. Sov. Math., 48:3 (1990), 329–336 | DOI | MR | Zbl | Zbl

[35] I.N. Sneddon, Fourier Transforms, Dover Books on Mathematics, Dover Publications, 1995 | MR

[36] Ukrainian. Math. J., 42:6 (1990), 758–760 | DOI | MR | Zbl

[37] E. Tsekanovskiĭ, “Characteristic Function and Sectorial Boundary-Value Problems”, Proceedings of the Institute of Mathematics (Novosibirsk), 7, 1987, 180–195 (Russian) | MR