Dirac systems with regular and singular transmission effects

Authors : Ekin UĞURLU

Pages : 193-210

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :In this paper, we investigate the spectral properties of singular eigenparameter dependent dissipative problems in Weyl`s limit-circle case with finite transmission conditions. In particular, these transmission conditions are assumed to be regular and singular. To analyze these problems we construct suitable Hilbert spaces with special inner products and linear operators associated with these problems. Using the equivalence of the Lax-Phillips scattering function and Sz-Nagy-Foiaş characteristic functions we prove that all root vectors of these dissipative operators are complete in Hilbert spaces.
Keywords : Dissipative operator, first order system, transmission condition, scattering function, characteristic function