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Multiple expansions in series of eigen- and associated functions of boundary eigenvalue problems nonlinearly dependent on the spectral parameter; Part I

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References

  1. A. Dijksma, H. Langer and H. de Snoo. Symmetric Sturm-Liouville operators with eigenvalue depending boundary conditions. Can. Math. Soc. Conference Proc. 8, 87–116 (1987).

    Google Scholar 

  2. G. Freiling. Boundary value problems associated with multiple roots of the characteristic equation. Results in Mathematics 11, 44–62 (1987).

    Article  MathSciNet  MATH  Google Scholar 

  3. G. Freiling. General boundary eigenvalue problems for systems of differential equations with multiple roots of the characteristic equation. Proc. Royal. Soc. Edingburgh 108A, 45–56 (1988).

    Article  MathSciNet  Google Scholar 

  4. G. Freiling. On the completeness and minimality of the derived chains of eigen- and associated functions of boundary eigenvalue problems non-linearly dependant on the parameter. Results in Mathematics 14, 64–83 (1988).

    Article  MathSciNet  MATH  Google Scholar 

  5. F.J. Kaufmann. Abgeleitete Birkhoff-Reihen bei Randeigenwertproblemen N(y) = λP(y) mit λ -abhängigen Randbedingungen. Mitteilungen Math. Sem. Giessen, Heft 190, 107 p. (1989).

  6. M.V. Keldysh. Completeness of characteristic functions of certain class of non-selfadjoint operators. Russ. Math. Surveys, 15–44 (1971); short version; Dokl. Akad. Nauk SSSR 77, 11–14 (1951).

  7. A.O. Kravitskii. Double expansion into series of eigenfunctions of certain nonsel-fadjoint boundary value problems. Diff. Equ. 4, 86–92 (1968).

    Google Scholar 

  8. R. Mennicken and M. Möller. Root functions of boundary eigenvalue operator functions. Integral Equ. and Operator Theory 9, 237–265 (1986).

    Article  MATH  Google Scholar 

  9. R. Mennicken and M. Möller. Boundary eigenvalue problems. In: Operator Theory and Systems. Proc. Workshop Amsterdam, ed.: I. Gohberg, H. Bart, M.A. Kaas-hoek; Birkhäuser, Stuttgart (1986).

    Google Scholar 

  10. M.A. Naimark. Linear differential operators, Part I and Part II. F. Ungar New York, 1967.

  11. M.B. Orazov and A.A. Shkalikov. The n-fold basis property of the characteristic functions of certain regular boundary-value problems. Sib. Math. J. 17, 483–492 (1976).

    Article  Google Scholar 

  12. A.S. Pechentsov. Boundary-value problems for differential equations with a parameter, having characteristic equations with multiple root. Diff. Equ. 20, 206–215 (1984).

    MathSciNet  MATH  Google Scholar 

  13. A.A. Shkalikov. Boundary value problems for ordinary differential equations with a parameter in the boundary conditions. Journal of Soviet Math. 33, 1311–1342 (1986), Transi, of: Trudy Sem. imeni Petrovskogo 9, 190–229 (1983).

    Google Scholar 

  14. A.A. Shkalikov. On properties of some of the eigenelements and associated elements of selfadjoint quadratic operator pencils. Soviet Mat. Dokl. 32, 298–304 (1985).

    MATH  Google Scholar 

  15. M.E. Wermuth. Konvergenzuntersuchungen bei Eigenfunktionsent Wicklungen zu Randeigenwertproblemen n-ter Ordnung mit parameterabhängigen Randbedingungen. Dissertation, Aachen (1984).

  16. R.M. Young. An Introduction to nonharmonic Fourier series. Acad. Press, New York 1980.

    MATH  Google Scholar 

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  1. Lehrstuhl II f. Mathematik für Ingenieure RWTH Aachen, Templergraben 55, D-5100, Aachen

    Gerhard Freiling

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  1. Gerhard Freiling
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Freiling, G. Multiple expansions in series of eigen- and associated functions of boundary eigenvalue problems nonlinearly dependent on the spectral parameter; Part I. Results. Math. 17, 83–99 (1990). https://doi.org/10.1007/BF03322632

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