The Discrete Self-Adjoint Dirac Systems of General Type: Explicit Solutions of Direct and Inverse Problems, Asymptotics of Verblunsky-Type Coefficients and the Stability of Solving of the Inverse Problem
We consider discrete self-adjoint Dirac systems determined by the potentials (sequences) {Ck} such that the matrices Ck are positive definite and j-unitary, where j is a diagonal m × m matrix which has m1 entries 1 and m2 entries –1 (m1 +m2 = m) on the main diagonal. We construct systems with the ra...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України
2018
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| Series: | Журнал математической физики, анализа, геометрии |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/145885 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The Discrete Self-Adjoint Dirac Systems of General Type: Explicit Solutions of Direct and Inverse Problems, Asymptotics of Verblunsky-Type Coefficients and the Stability of Solving of the Inverse Problem / I. Roitberg, A. Sakhnovich // Журнал математической физики, анализа, геометрии. — 2018. — Т. 14, № 4. — С. 532-548. — Бібліогр.: 22 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | We consider discrete self-adjoint Dirac systems determined by the potentials (sequences) {Ck} such that the matrices Ck are positive definite and j-unitary, where j is a diagonal m × m matrix which has m1 entries 1 and m2 entries –1 (m1 +m2 = m) on the main diagonal. We construct systems with the rational Weyl functions and explicitly solve the inverse problem to recover systems from the contractive rational Weyl functions. Moreover, we study the stability of this procedure. The matrices Ck (in the potentials) are the so-called Halmos extensions of the Verblunsky-type coefficients ρk. We show that in the case of the contractive rational Weyl functions the coefficients ρk tend to zero and the matrices Ck tend to the identity matrix Im. |
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