Seven Papers Translated from the Russian

Kovalishina, I. V.; Potapov, Viktor

doi:10.1090/trans2/138

Cited by 17 publications

(18 citation statements)

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“…One of them was based on Potapov's method (which characterizes the solutions of an interpolation problem in terms of a related fundamental matrix inequality; see e.g. [41]) suitably adapted to the present framework. The next theorem extends that analysis (especially [15,Lemma 3.5]) and characterizes all the solutions of the aBIP in terms of positive kernels and in terms of the reproducing kernel Hilbert spaces H(S).…”

Section: Fundamental Matrix Inequalitiesmentioning

confidence: 99%

On boundary interpolation for matrix valued Schur functions

Bolotnikov¹,

Dym²

2006

Memoirs of the AMS

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Section: Fundamental Matrix Inequalitiesmentioning

confidence: 99%

On boundary interpolation for matrix valued Schur functions

Bolotnikov¹,

Dym²

2006

Memoirs of the AMS

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“…Degenerate cases of the classical Nevanlinna-Pick and Carathéodory-Fejér interpolation problems for Schur functions were studied using quite different approaches in [9], [10], [11] and [13,Section 7]. The results obtained below in Section 7 rely on Potapov's method (which characterizes the solutions of an interpolation problem in terms of a related fundamental matrix inequality suitably adapted to the present framework; for some early examples of this method, see [27]). …”

Section: (T T)mentioning

confidence: 99%

On degenerate interpolation, entropy and extremal problems for matrix Schur functions

Bolotnikov

Dym

1998

Integr equ oper theory

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We consider a general bitangential interpolation problem for matrix Schur functions and focus mainly on the case when the associated Pick matrix is singular (and positive semidefinite). Descriptions of the set of all solutions are given in terms of special linear fractional transformations which are obtained using two quite different approaches. As applications of the obtained results we consider the maximum entropy and the maximum determinant extension problems suitably adapted to the degenerate situation.

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“…The first develops Potapov's method (which characterizes the solutions of an interpolation problem in terms of a related fundamental matrix inequality [11]), and the second is related to reproducing kernel methods in interpolation theory [10].…”

Section: The Main Resultsmentioning

confidence: 99%

Interpolation for multipliers on reproducing kernel Hilbert spaces

Bolotnikov

2002

Proc. Amer. Math. Soc.

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Abstract. All solutions of a tangential interpolation problem for contractive multipliers between two reproducing kernel Hilbert spaces of analytic vectorvalued functions are characterized in terms of certain positive kernels. In a special important case when the spaces consist of analytic functions on the unit ball of C d and the reproducing kernels are of the form (1 − z, w −1 )Ip and (1 − z, w ) −1 Iq, the characterization leads to a parametrization of the set of all solutions in terms of a linear fractional transformation.

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Seven Papers Translated from the Russian

Cited by 17 publications

References 0 publications

On boundary interpolation for matrix valued Schur functions

On boundary interpolation for matrix valued Schur functions

On degenerate interpolation, entropy and extremal problems for matrix Schur functions

Interpolation for multipliers on reproducing kernel Hilbert spaces

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