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Singuläre S-hermitesche Rand-Eigenwertprobleme

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Abstract

The theory of singular self-adjoint eigenvalue problems developed by Weyl [13], Stone [12], Kodaira [2] and others has been generalized by A. Schneider [8], [9], [10], [11] to real S-hermitian systems of differential equations with real boundary conditions. Here the theory of singular S-hermitian boundary-value problems for arbitrary complex systems of differential equations with complex boundary conditions is developed. Moreover the boundary conditions are allowed to depend linearly on the eigenvalue-parameter.

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Literatur

  1. CODDINGTON, E. A.: Generalized resolutions of the identity for symmetric ordinary differential operators. Ann. of Math. 68, 378–392 (1958).

    Google Scholar 

  2. KODAIRA, K.: On ordinary differential equations of any even order and the corresponding eigenfunction expansions. Amer. J. Math. 72, 502–544 (1950).

    Google Scholar 

  3. NEUMARK, M. A.: Lineare Differentialoperatoren, 2. Aufl. Berlin: Akademie-Verlag 1963.

    Google Scholar 

  4. NIESSEN, H.-D. u. R. MENNICKEN: (S,\(\tilde S\))-adjungierte Randwertoperatoren. Erscheint in Math. Nachr.

  5. SCHÄFKE, F. W. u. A. SCHNEIDER: S-hermitesche Rand-Eigenwertprobleme I. Math. Ann. 162, 9–26 (1965).

    Google Scholar 

  6. SCHÄFKE, F. W. u. A. SCHNEIDER: S-hermitesche Rand-Eigenwertprobleme II. Math. Ann. 165, 236–260 (1966).

    Google Scholar 

  7. SCHÄFKE, F. W. u. A. SCHNEIDER: S-hermitesche Rand-Eigenwertprobleme III. Math. Ann. 177, 67–94 (1968).

    Google Scholar 

  8. SCHNEIDER, A.: Untersuchungen über singuläre reelle S-hermitesche Differentialgleichungssysteme im Normalfall. Math. Z. 107, 271–296 (1968).

    Google Scholar 

  9. SCHNEIDER, A.: Weitere Untersuchungen über singuläre reelle S-hermitesche Differentialgleichungssysteme im Normalfall. Math. Z. 109, 153–168 (1969).

    Google Scholar 

  10. SCHNEIDER, A.: Zum Entwicklungssatz bei reellen singulären Differentialgleichungssystemen. Erscheint demnächst.

  11. SCHNEIDER, A.: Bemerkungen über singuläre reelle S-hermitesche Differentialgleichungssysteme. Erscheint demnächst.

  12. STONE, M. H.: Linear transformations in Hilbert space. Amer. Math. Soc. Coll. Publ. 15 (1932).

  13. WEYI, H.: Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen. Math. Ann. 68, 220–269 (1910).

    Google Scholar 

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Niessen, HD. Singuläre S-hermitesche Rand-Eigenwertprobleme. Manuscripta Math 3, 35–68 (1970). https://doi.org/10.1007/BF01168461

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