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Tytuł artykułu

On some extensions of the a-model

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Języki publikacji
EN
Abstrakty
EN
The A-model for finite rank singular perturbations of class [formula], is considered from the perspective of boundary relations. Assuming further that the Hilbert spaces [formula] admit an orthogonal decomposition [formula], with the corresponding projections satisfying [formula], nontrivial extensions in the A-model are constructed for the symmetric restrictions in the subspaces.
Rocznik
Strony
569--597
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
  • Vilnius University Institute of Theoretical Physics and Astronomy Sauletekio Ave. 3, LT-10257 Vilnius, Lithuania
Bibliografia
  • [1] S. Albeverio, S.-M. Fei, P. Kurasov, Many body problems with “spin”-related contact interactions, Rep. Math. Phys. 47 (2001) 2, 157-166.
  • [2] S. Albeverio, P. Kurasov, Singular Perturbations of Differential Operators, London Mathematical Society Lecture Note Series 271, Cambridge University Press, UK, 2000.
  • [3] Y. Arlinskii, S. Belyi, V. Derkach, E. Tsekanovskii, On realization of the Krein-Langer class Nk of matrix-valued functions in Pontryagin spaces, Math. Nachr. 281 (2008) 10, 1380-1399.
  • [4] T. Azizov, I. Iokhvidov, Linear Operators in Spaces with an Indefinite Metric, John Wiley & Sons, Inc., 1989.
  • [5] J. Behrndt, V.A. Derkach, S. Hassi, H. de Snoo, A realization theorem for generalized Nevanlinna families, Operators and Matrices 5 (2011) 4, 679-706.
  • [6] J. Behrndt, S. Hassi, H. de Snoo, Functional models for Nevanlinna families, Opuscula Math. 28 (2008) 3, 233-245.
  • [7] J. Behrndt, A. Luger, C. Trunk, On the negative squares of a class of self-adjoint extensions in Krein spaces, Math. Nachr. 286 (2013) 2-3, 118-148.
  • [8] V. Derkach, On Weyl function and generalized resolvents of a Hermitian operator in a Krein space, Integr. Equ. Oper. Theory 23 (1995) 4, 387-415.
  • [9] V. Derkach, Boundary triplets, Weyl functions, and the Krein formula, volume 1-2 of Operator Theory, Springer, Basel, 2015, Chapter 10, 183-218.
  • [10] V.A. Derkach, S. Hassi, A reproducing kernel space model for NK-functions, Proc. Amer. Math. Soc. 131 (2003) 12, 3795-3806.
  • [11] V. Derkach, S. Hassi, M. Malamud, Generalized boundary triples, I. Some classes of isometric and unitary boundary pairs and realization problems for subclasses of Nevanlinna functions, Math. Nachr. 293 (2020) 7, 1278-1327.
  • [12] V. Derkach, S. Hassi, M. Malamud, H. de Snoo, Boundary relations and their Weyl families, Trans. Amer. Math. Soc. 358 (2006) 12, 5351-5400.
  • [13] V. Derkach, S. Hassi, M. Malamud, H. de Snoo, Boundary relations and generalized resolvents of symmetric operators, Russ. J. Math. Phys. 16 (2009) 1, 17-60.
  • [14] V. Derkach, S. Hassi, M. Malamud, H. de Snoo, Boundary triplets and Weyl functions. Recent developments, [in:] S. Hassi, H.S.V. de Snoo, F.H. Szafraniec (eds), Operator Methods for Boundary Value Problems, London Math. Soc. Lecture Note Series, vol. 404, Cambridge University Press, UK, 2012, Chapter 7, 161-220.
  • [15] A. Dijksma, P. Kurasov, Yu. Shondin, High order singular rank one perturbations of a positive operator, Integr. Equ. Oper. Theory 53 (2005), 209-245.
  • [16] A. Dijksma, H. Langer, Y. Shondin, Rank one perturbations at infinite coupling in Pontryagin spaces, J. Func. Anal. 209 (2004) 1, 206-246.
  • [17] A. Dijksma, Y. Shondin, Singular point-like perturbations of the Bessel operator in a Pontryagin space, J. Diff. Equ. 164 (2000) 1, 49-91.
  • [18] S. Hassi, H.S.V. de Snoo, F.H. Szafraniec, Componentwise and Cartesian decompositions of linear relations, Dissertationes Math. 465 (2009), 1-59.
  • [19] S. Hassi, H.S.V. de Snoo, F.H. Szafraniec, Infinite-dimensional perturbations, maximal ly nondensely defined symmetric operators, and some matrix representations, Indag. Math. 23 (2012) 4, 1087-1117.
  • [20] S. Hassi, S. Kuzhel, On symmetries in the theory of finite rank singular perturbations, J. Func. Anal. 256 (2009), 777-809.
  • [21] S. Hassi, M. Malamud, V. Mogilevskii, Unitary equivalence of proper extensions of a symmetric operator and the Weyl function, Integr. Equ. Oper. Theory 77 (2013) 4, 449-487.
  • [22] S. Hassi, Z. Sebestyen, H.S.V. de Snoo, F.H. Szafraniec, A canonical decomposition for linear operators and linear relations, Acta Math. Hungar. 115 (2007) 4, 281-307.
  • [23] R. Jursenas, Computation of the unitary group for the Rashba spin-orbit coupled operator, with application to point-interactions, J. Phys. A: Math. Theor. 51 (2018) 1, 015 203.
  • [24] R. Jursenas, The peak model for the triplet extensions and their transformations to the reference Hilbert space in the case of finite defect numbers, arXiv:1810.07 416, 2020.
  • [25] P. Kurasov, H-n-perturbations of self-adjoint operators and Krein’s resolvent formula, Integr. Equ. Oper. Theory 45 (2003) 4, 437-460.
  • [26] P. Kurasov, Triplet extensions I: Semibounded operators in the scale of Hilbert spaces, Journal d’Analyse Mathematique 107 (2009) 1, 252-286.
  • [27] P. Kurasov, Yu.V. Pavlov, On field theory methods in singular perturbation theory, Lett. Math. Phys. 64 (2003) 2, 171-184.
  • [28] K. Schmudgen, Unbounded Self-adjoint Operators on Hilbert Space, Springer, Dordrecht, Heidelberg, New York, London, 2012.
Uwagi
PL
Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-821b6fad-a005-46f3-b71b-86ca97fb5190
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