PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
Powiadomienia systemowe
  • Sesja wygasła!
Tytuł artykułu

Krein-von Neumann extension of an even order differential operator on a finite interval

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We describe the Krein-von Neumann extension of minimal operator associated with the expression [formula] on a finite interval (a, b) in terms of boundary conditions. All non-negative extensions of the operator A as well as extensions with a finite number of negative squares are described.
Rocznik
Strony
681--698
Opis fizyczny
Bibliogr. 33 poz.
Twórcy
  • NAS of Ukraine Institute of Applied Mathematics and Mechanics, Ukraine
  • Donetsk National University, Donetsk, Ukraine
Bibliografia
  • [1] N.I. Akhiezer, I.M. Glazman, Theory of Linear Operators in Hilbert Spaces, Nauka, Moscow, 1978.
  • [2] A.Yu. Ananieva, V.S. Budyika, To the spectral theory of the Bessel operator on finite interval and half-line, J. of Math. Scien. 211 (2015) 5, 624-645.
  • [3] T. Ando, K. Nishio, Positive selfadjoint extensions of positive symmetric operators, Tohoku Math. J. 22 (1970), 65-75.
  • [4] M.S. Ashbaugh, F. Gesztesy, M. Mitrea, R. Shterenberg, G. Teschl, Spectral theory for perturbed Krein Laplacians in nonsmooth domains, Adv. Math. 223 (2010), 1372-1467.
  • [5] M.S. Ashbaugh, F. Gesztesy, M. Mitrea, R. Shterenberg, G. Teschl, The Krein-von Neumann extension and its connection to an abstract buckling problem, Math. Nachr. 283 (2010) 2, 165-179.
  • [6] M.S. Ashbaugh, F. Gesztesy, M. Mitrea, R. Shterenberg, G. Teschl, A survey of the Krein-von Neumann extension, the corresponding abstract buckling problem, and Weyl-type spectral asymptotics for perturbed Krein Laplacians in non smooth domains, [in:] M. Demuth and W. Kirsh (eds.), Mathematical Physics, Spectral Theory and Stochastic Analysys, Operator Theory: Advances and Applications 232, Birkhauser, Springer, Basel (2013), 1-106.
  • [7] J. Behrndt, F. Gesztesy, T. Micheler, M. Mitrea, The Krein-von Neumann realization of perturbed Laplacians on bounded Lipschitz domains, Operator Theory: Advances and Applications 255, Birkhauser, Springer, Basel (2016), 49-66.
  • [8] J. Behrndt, T. Micheler, Elliptic differential operators on Lipschitz domains and abstract boundary value problems, J. Funct. Anal. 267 (2014), 3657-3709.
  • [9] M.Sh. Birman, Perturbations of the continuous spectrum of a singular elliptic operator by varying the boundary and the boundary conditions, Vestnik Leningrad Univ. 17 (1962) 1, 22-55 [in Russian]; transl. in Spectral Theory of Differential Operators: M. Sh. Birman 80th Anniversary Collection, T. Suslina and D. Yafaev (eds.), AMS Translation, Ser. 2, Advances in the Mathematical Sciences 225, Amer. Math. Soc, Providence, RI (2008), 19-53.
  • [10] B.M. Brown, J.S. Christiansen, On the Krein and Friedrichs extension of a positive Jacobi operator, Expo. Math. 23 (2005), 176-186.
  • [11] L. Bruneau, J. Dereziński, V. Georgescu, Homogeneous Schrodinger Operators on Half-line, Ann. Henri Poincare 12 (2011), 547-590.
  • [12] V.A. Derkach, M.M. Malamud, Generalized rezolvent and the boundary value problems for Hermitian operators with gaps, J. Funct. Anal. 95 (1991) 1, 1-95.
  • [13] V.A. Derkach, M.M. Malamud, Characteristic of almost solvable extensions of a Hermitian operators, Ukr. Mat. Zh. 44 (1992) 4, 435-459.
  • [14] V.A. Derkach, M.M. Malamud, The extension theory of Hermitian operators and the moment problem, J. Math. Sci. (New York) 73 (1995), 141-242.
  • [15] V.A. Derkach, M.M. Malamud, Extension theory of symmetric operators and boundary value problems, Proceedings of Institute of Mathematics of NAS of Ukraine 104 (2017) [in Russian].
  • [16] J. Eckhardt, F. Gesztesy, R. Nichols, G. Teschl, Weyl-Titchmarsh Theory for Sturm-Liouville Operators With Distributional Potentials, Opuscula Math. 33 (2013) 3, 467-563.
  • [17] W.N. Everitt, H. Kalf, The Bessel differential equation and the Hankel transform, Jour, of Comput. and App. Math. 208 (2007), 3-19.
  • [18] H. Freudental, Uber die Friedrichsche Fortsetzung halbbeschrankter Hermitescher Ope.ru-toren, Kon. Akad. Wetensch., Amsterdam, Proc. 39 (1936), 832-833.
  • [19] C. Fulton, Titchmarsh-Weyl m-functions for second-order Sturm-Liouville problems with two singular endpoints, Math. Nachr. 281 (2008) 10, 1418-1475.
  • [20] C. Fulton, H. Langer, Sturm-Liouville operators with singularities and generalized Nevanlinna functions, Complex Analysis and Operator Theory 4 (2010) 2, 179-243.
  • [21] F. Gesztesy, M. Mitrea, A description of all self-adjoint extensions of the laplacian and Krein-type resolvent formulas on non-smooth domains, J. Analyse Math. 113 (2011), 53-172.
  • [22] F. Gesztesy, M. Mitrea, Robin-to-Robin maps and Krein-type resolvent formulas for Schrodinger operators on bounded Lipschitz domains, [in:] V. Adamyan, Y.M. Berezansky, I. Gohberg, M.L. Gorbachuk, V. Gorbachuk, A.N. Kochubei, H. Langer, and G. Popov (eds.), Modern Analysis and Applications. The Mark Krein Centenary Conference 2, Operator Theory: Advances and Applications, vol. 191, Birkhauser, Basel, 2009, 81-113.
  • [23] V.I. Gorbachuk, M.L. Gorbachuk, Boundary Value Problems for Operator Differential Equations, Mathematics and its Applications (Soviet Series), vol. 48, Kluwer Academic Publishers Group, Dordrecht, 1991.
  • [24] G. Grubb, A characterization of the non-local boundary value problems associated with an elliptic operator, Ann. Scuola Norm. Sup. Pisa 22 (1968) 3, 425-513.
  • [25] G. Grubb, Spectral asymptotics for the "soft" self adjoint extension of a symmetric elliptic differential operator, J. Operator Th. 10 (1983), 9-20.
  • [26] S. Hassi, M. Malamud, H. de Snoo, On Krein's extension theory of nonnegative operators, Math. Nachr. 274-275 (2004), 40-73.
  • [27] H. Kalf, A characterization of the Friedrichs extension of Sturm-Liouville operators, J. London Math. Soc. 17 (1978) 2, 511-521.
  • [28] T. Kato, Perturbation Theory for Linear Operators, Springer-Verlag, Berlin, Heidelberg, New York, 1966.
  • [29] M.G. Krein, The theory of self-adjoint extensions of semibounded Hermitian transformations and its applications, I, Sb. Math. 20 (1947) 3, 431-495; II, ibid., 21 3, 365-404 [in Russian].
  • [30] A.A. Lunyov, Spectral functions of the simplest even order ordinary differential operator, Methods of Functional Analysis and Topology 19 (2013) 4, 319-326.
  • [31] M.M. Malamud, Spectral theory of elliptic operators in exterior domains, Russ. J. Math. Phys. 17 (2010), 96-125.
  • [32] M.M. Malamud, H. Neidhardt, Sturm-Liouville boundary value problems with operator potentials and unitary equivalence, J. Differential Equations 252 (2012), 5875-5922.
  • [33] J. von Neumann, Allqe.me.ine Eiqe.nwe.rtthe.orie Hermitescher Funktionaloperatoren, Math. Ann. 102 (1929), 49-131.
  • [34] F.S. Rofe-Beketov, Self-adjoint extensions of differential operators in a space of vector-valued functions, Teor. Funkcii Funkcional. Anal, i Prilozen. 8 (1969), 3-24 [in Russian].
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-676e93e9-df5e-4b86-811e-a45f2ac78e40
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.