Sampling of Discontinuous Dirac Systems

Abstract

In this article, we study discontinuous regular Dirac systems with transmission conditions at the point of discontinuity. We study briey the spectral analysis of problem as Levitan and Sargsjan [23]. In the special case, when our problem is continuous, the obtained results coincide with the corresponding results in Abd-Alla and Annaby [1] and Zayed and Garcia [30]. We derive sampling representations for transforms whose kernels are either solutions or Green's functions.

Keywords:

• Dirac systems
• Discontinuous boundary value problems
• Green's function
• Sampling theory
• Transmission conditions

Mathematics Subject Classification:

• 34L16
• 94A20
• 65L15

ACKNOWLEDGMENTS

The authors would like to thank the referees for their careful reading of the manuscript and constructive comments.