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On sampling and Dirac systems with eigenparameter in the boundary conditions

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Abstract

This paper investigates the sampling theory of signal analysis associated with Dirac systems when the eigenvalue parameter appears linearly in the boundary conditions. We briefly study the spectral analysis of the problem as in Levitan and Sargsjan (Translations of Mathematical Monographs, vol. 39, 1975; Sturm-Liouville and Dirac Operators, 1991) in away similar to that of Fulton (Proc. R. Soc. Edinb., A 77:293–308, 1977) and Kerimov (Differential Equations 38(2):164–174, 2002). We study the two different cases when the eigenparameter appears in one and in two conditions.

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Authors and Affiliations

  1. Department of Mathematics, Statistics & Physics, Qatar University, P.O. Box 2713, Doha, Qatar

    M. H. Annaby

  2. Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt

    M. H. Annaby

  3. Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    M. M. Tharwat

Authors
  1. M. H. Annaby
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  2. M. M. Tharwat
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Correspondence to M. H. Annaby.

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Annaby, M.H., Tharwat, M.M. On sampling and Dirac systems with eigenparameter in the boundary conditions. J. Appl. Math. Comput. 36, 291–317 (2011). https://doi.org/10.1007/s12190-010-0404-9

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  • DOI: https://doi.org/10.1007/s12190-010-0404-9

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