On a new class of structured matrices related to the discrete skew-self-adjoint Dirac systems

Fritzsche, Bernd; Kirstein, Bernd; Sakhnovich, Alexander

doi:10.13001/1081-3810.1277

Cited by 3 publications

(1 citation statement)

References 20 publications

(14 reference statements)

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“…This identity differs from the identity [35,36] for an operator with difference kernel. Matrices satisfying a discrete analogue of (3.15) were treated in [17]. The operator identity (3.15) for the case, when k in (1.3) is a vector, was studied in [25].…”

Section: By (38) the Equalitymentioning

confidence: 99%

Semiseparable Integral Operators and Explicit Solution of an Inverse Problem for a Skew-Self-Adjoint Dirac-Type System

Fritzsche

Kirstein

Sakhnovich

2010

Integr. Equ. Oper. Theory

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Inverse problem to recover the skew-self-adjoint Dirac-type system from the generalized Weyl matrix function is treated in the paper. Sufficient conditions under which the unique solution of the inverse problem exists, are formulated in terms of the Weyl function and a procedure to solve the inverse problem is given. The case of the generalized Weyl functions of the form φ(λ) exp{−2iλD}, where φ is a strictly proper rational matrix function and D = D * ≥ 0 is a diagonal matrix, is treated in greater detail. Explicit formulas for the inversion of the corresponding semiseparable integral operators and recovery of the Dirac-type system are obtained for this case.Mathematics Subject Classification (2010). Primary 34A55; Secondary 34B20; 47G10; 34A05.

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Section: By (38) the Equalitymentioning

confidence: 99%

Semiseparable Integral Operators and Explicit Solution of an Inverse Problem for a Skew-Self-Adjoint Dirac-Type System

Fritzsche

Kirstein

Sakhnovich

2010

Integr. Equ. Oper. Theory

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Operator identities corresponding to inverse problems for Dirac systems

Fritzsche

Kirstein

Roitberg

et al. 2012

Indagationes Mathematicae

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The structured operators and corresponding operator identities, which appear in inverse problems for the self-adjoint and skew-selfadjoint Dirac systems with rectangular potentials, are studied in detail. In particular, it is shown that operators with the close to displacement kernels are included in this class. A special case of positive and factorizable operators is dealt with separately. MSC(2010): 45H05, 47G10, 34L40, 47A68.

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Discrete Dirac system: rectangular Weyl functions, direct and inverse problems

Fritzsche¹,

Kirstein²,

Roitberg³

et al. 2014

Operators and Matrices

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Abstract.A transfer matrix function representation of the fundamental solution of the generaltype discrete Dirac system, corresponding to rectangular Schur coefficients and Weyl functions, is obtained. Connections with Szegö recurrence, Schur coefficients and structured matrices are treated. A Borg-Marchenko-type uniqueness theorem is derived. Inverse problems on the interval and semi-axis are solved.Mathematics subject classification (2010): 34B20, 34L40, 39A12, 47A57.

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On a new class of structured matrices related to the discrete skew-self-adjoint Dirac systems

Cited by 3 publications

References 20 publications

Semiseparable Integral Operators and Explicit Solution of an Inverse Problem for a Skew-Self-Adjoint Dirac-Type System

Semiseparable Integral Operators and Explicit Solution of an Inverse Problem for a Skew-Self-Adjoint Dirac-Type System

Operator identities corresponding to inverse problems for Dirac systems

Discrete Dirac system: rectangular Weyl functions, direct and inverse problems

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