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The sum of matrix nevanlinna functions and self-adjoint extensions in exit spaces

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Recent Progress in Operator Theory

Part of the book series: Operator Theory Advances and Applications ((OT,volume 103))

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Abstract

For a closed symmetric operator or relation, Kre 137-1 n’s formula describes all its self-adjoint extensions in terms of certain holomorphic parameters. Our interest is in self-adjoint extensions of a symmetric relation which extends itself an orthogonal sum of two symmetric relations. The corresponding class of parameters in Kre 137-2 n’s formula is idcntificd. This leads to a description of (minimal) self-adjoint extensions in a fixed exit space.

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References

  1. Alpay, D., Bruinsma, P., Dijksma, A., DE Snoo, H.S.V.: Interpolation problems, extensions of symmetric operators and reproducing kernel spaces I; Operator Theory: Adv. Appl. 50 (1991), 35–82.

    Google Scholar 

  2. Alpay, D., Bruinsma, P., Dijksma, A., DE Snoo, H.S.V.: Interpolation problems, extensions of symmetric operators and reproducing kernel spaces II; Integral Equations Operator Theory 14 (1991), 465-500, 15 (1992), 378–388.

    Article  Google Scholar 

  3. Ando, T.: Reproducing kernel spaces and quadratic inequalities; Lecture notes, Hokkaido University, Sapporo 1987.

    MATH  Google Scholar 

  4. Bruinsma, P.: Interpolation problems for Schur and Nevanlinna pairs; Doctoral dissertation, Groningen 1991.

    Google Scholar 

  5. Bruinsma, P.: Degenerate interpolation problems for Nevanlinna pairs; Indag. Math., N.S. 2(2) (1991), 179–200.

    Article  MathSciNet  MATH  Google Scholar 

  6. Coddington, E.A.: Extension theory of formally normal and symmetric subspaces; Mem. Amer. Math. Soc. 134, Providence, R.I. 1973.

    Google Scholar 

  7. Coddington, E.A., Levinson, N.: Theory of ordinary differential equations; McGraw-Hill, New York Toronto London 1955.

    MATH  Google Scholar 

  8. Derkach, V.A.: On Weyl function and generalized resolvents of a hermitian operator in a Krein space; Integral Equations Operator Theory 23 (1995), 387–415.

    Article  MathSciNet  MATH  Google Scholar 

  9. Derkach, V.A., Malamud, M.M.: Generalized resolvents and the boundary value problems for hermitian operators with gaps; J. Funct. Anal. 95 (1991), 1–95.

    Article  MathSciNet  MATH  Google Scholar 

  10. Derkach, V.A., Malamud, M.M.: The extension theory of hermitian operators and the moment problem; J. Math. Sciences 73 (1995), 141–242.

    Article  MathSciNet  MATH  Google Scholar 

  11. Duksma, A., Langer, H., DE Snoo, H.S.V.: Eigenvalues and pole functions of Hamiltonian systems and eigenvalue depending boundary conditions; Math. Nachr. 161 (1993), 107–154.

    Article  MathSciNet  Google Scholar 

  12. Dijksma, A., DE Snoo, H.S.V.: Selfadjoint extensions of symmetric subspaces; Pacific J. Math. 54 (1974), 71–99.

    MathSciNet  MATH  Google Scholar 

  13. Hassi, S., Langer, H., DE Snoo, H.S.V.: Selfadjoint extensions for a class of symmetric operators with defect numbers (1,1); 15th OT Conference Proceedings (1995), 115–145.

    Google Scholar 

  14. Hille, E.: Lectures on ordinary differential equations; Addison-Wesley, Reading, Menlo Park London Don Mills 1969.

    MATH  Google Scholar 

  15. Katsnelson, V.: Methods of J-theory in continuous interpolation problems of analysis; Part I, VINITI, Kharkov 1982 (in Russian), English translation by T. Ando, Sapporo 1985.

    Google Scholar 

  16. Krein, M.G., Langer, H.: Defect subspaces and generalized resolvents of an hermitian operator in the space II κ; Funct. Anal. Appl. 5 (1971), 136–146, 217-228.

    Article  MATH  Google Scholar 

  17. Langer, H., Textorius, B.: On generalized resolvents and Q-functions of symmetric linear relations (subspaces) in Hilbert space; Pacific J. Math. 72 (1977), 135–165.

    MathSciNet  MATH  Google Scholar 

  18. Langer, H., Textorius, B.: L-resolvent matrices of symmetric linear relations with equal defect numbers; applications to canonical differential equations; Integral Equations Operator Theory 5 (1982), 208–243.

    Article  MathSciNet  MATH  Google Scholar 

  19. Nudelman, A.A.: On a generalization of classical interpolation problems; Dokl. Akad. Nauk SSSR 256 (1981), 790–793 (in Russian), English translation: Sov. Math. Dokl. 23 (1981), 125-128.

    MathSciNet  Google Scholar 

  20. Pavlov, B.S.: The theory of extensions and explicitly-soluble models; Russian Math. Surveys 42:6 (1987), 127–168.

    Article  MATH  Google Scholar 

  21. Titchmarsh, E.C.: Eigenfunction expansions associated with second-order differential equations, Part One, second edition, Oxford University Press, Oxford 1962.

    Google Scholar 

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Hassi, S., Kaltenbäck, M., de Snoo, H.S.V. (1998). The sum of matrix nevanlinna functions and self-adjoint extensions in exit spaces. In: Gohberg, I., Mennicken, R., Tretter, C. (eds) Recent Progress in Operator Theory. Operator Theory Advances and Applications, vol 103. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8793-9_8

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  • DOI: https://doi.org/10.1007/978-3-0348-8793-9_8

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9776-1

  • Online ISBN: 978-3-0348-8793-9

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