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On Spectral Synthesis for Dissipative Dirac Type Operators

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Abstract

The paper is concerned with the spectral synthesis for general dissipative boundary value problems for n × n first order systems of ordinary differential equations on a finite interval. We show that the resolvent of any complete dissipative Dirac type operator with summable potential admits the spectral synthesis in \({L^2([0,1]; \mathbb{C}^n)}\). Moreover, we provide explicit sufficient conditions for Dirac type operator to be complete and dissipative.

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  1. Institute of Applied Mathematics and Mechanics NAS of Ukraine, Roza Luksemburg str. 74, 83114, Donetsk, Ukraine

    Anton A. Lunyov & Mark M. Malamud

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  1. Anton A. Lunyov
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  2. Mark M. Malamud
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Lunyov, A.A., Malamud, M.M. On Spectral Synthesis for Dissipative Dirac Type Operators. Integr. Equ. Oper. Theory 80, 79–106 (2014). https://doi.org/10.1007/s00020-014-2154-9

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