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This article is cited in 2 scientific papers (total in 2 papers)
Description of Generalized Resolvents and Characteristic Matrices of Differential Operators in Terms of the Boundary Parameter
V. I. Mogilevskii Luhansk Taras Schevchenko State Pedagogical University
Abstract:
We supplement and further develop well-known results due to Shtraus on the generalized resolvents and spectral functions of the minimal operator $L_0$ generated by a formally self-adjoint differential expression of even order with operator coefficients given on the interval $[0,b\rangle$, where $b\le\infty$. Our approach is based on the notion of a disintegrating boundary triple, which allows us to establish a relation between the Shtraus method and boundary-value problems with spectral parameter in the boundary condition. In particular, we obtain a parametrization of all the characteristic matrices $\Omega(\lambda)$ of the operator $L_0$ in terms of the spectral parameter corresponding to a boundary-value problem. Such a parametrization is given as a block representation of the matrix $\Omega(\lambda)$, as well as by formulas similar to Krein's well-known formula for generalized resolvents.
Keywords:
differential operator of even order, minimal operator, self-adjoint operator, generalized resolvent, characteristic matrix, boundary-value problem, deficiency index, boundary triple, holomorphic function, Nevanlinna function, Weyl function.
Received: 20.09.2009 Revised: 05.11.2010
Citation:
V. I. Mogilevskii, “Description of Generalized Resolvents and Characteristic Matrices of Differential Operators in Terms of the Boundary Parameter”, Mat. Zametki, 90:4 (2011), 558–583; Math. Notes, 90:4 (2011), 548–570
Linking options:
https://www.mathnet.ru/eng/mzm8538https://doi.org/10.4213/mzm8538 https://www.mathnet.ru/eng/mzm/v90/i4/p558
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Abstract page: | 469 | Full-text PDF : | 183 | References: | 76 | First page: | 14 |
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