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arXiv math/0511594math.SPmath-phmath.MP
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斜自伴离散和连续Dirac型系统:反问题和Borg-Marchenko定理

Skew-self-adjoint discrete and continuous Dirac type systems: inverse problems and Borg-Marchenko theorems

Alexander Sakhnovich

摘要:

得到了连续斜自伴Dirac型系统反问题的新公式。对于离散的斜自伴Dirac型系统,还得到了一般型谱逆问题的Weyl函数解。给出了区间上Weyl函数的描述.对于离散和连续的非自伴系统,也得到了Borg-Marchenko型唯一性定理。

英文摘要:

New formulas on the inverse problem for the continuous skew-self-adjoint Dirac type system are obtained. For the discrete skew-self-adjoint Dirac type system the solution of a general type inverse spectral problem is also derived in terms of the Weyl functions. The description of the Weyl functions on the interval is given. Borg-Marchenko type uniqueness theorems are derived for both discrete and continuous non-self-adjoint systems too.

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