Illinois Journal of Mathematics

Extensions, dilations and functional models of discrete Dirac operators

B. P. Allahverdiev

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A space of boundary values is constructed for minimal symmetric discrete Dirac operators in the limit-circle case. A description of all maximal dissipative, maximal accretive and self-adjoint extensions of such a symmetric operator is given in terms of boundary conditions at infinity. We construct a self-adjoint dilation of a maximal dissipative operator and its incoming and outgoing spectral representations, which make it possible to determine the scattering matrix of the dilation. We also construct a functional model of the dissipative operator and its characteristic function. Finally, we prove the completeness of the system of eigenvectors and associated vectors of dissipative operators.

Article information

Illinois J. Math., Volume 47, Number 3 (2003), 831-845.

First available in Project Euclid: 13 November 2009

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Zentralblatt MATH identifier

Primary: 47B39: Difference operators [See also 39A70]
Secondary: 47A40: Scattering theory [See also 34L25, 35P25, 37K15, 58J50, 81Uxx] 47A45: Canonical models for contractions and nonselfadjoint operators 47B25: Symmetric and selfadjoint operators (unbounded) 47B44: Accretive operators, dissipative operators, etc.


Allahverdiev, B. P. Extensions, dilations and functional models of discrete Dirac operators. Illinois J. Math. 47 (2003), no. 3, 831--845. doi:10.1215/ijm/1258138196.

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