On Spectral Synthesis for Dissipative Dirac Type Operators

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.