The Schur Transformation for Generalized Nevanlinna Functions: Interpolation and Self-Adjoint Operator Realizations
نویسندگان
چکیده
منابع مشابه
The Schur Transformation for Nevanlinna Functions: Operator Representations, Resolvent Matrices, and Orthogonal Polynomials
A Nevanlinna function is a function which is analytic in the open upper half plane and has a non-negative imaginary part there. In this paper we study a fractional linear transformation for a Nevanlinna function n with a suitable asymptotic expansion at ∞, that is an analogue of the Schur transformation for contractive analytic functions in the unit disc. Applying the transformation p times we ...
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The nondegenerate Nevanlinna-Pick-Carathéodory-Fejer interpolation problem with finitely many interpolation conditions always has infinitely many solutions in a generalized Schur class Sκ for every κ ≥ κmin where the integer κmin equals the number of negative eigenvalues of the Pick matrix associated to the problem and completely determined by interpolation data. A linear fractional description...
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is positive semidefinite for every choice of an integer n and of n points z1, . . . , zn ∈ D. The significance of this characterization for interpolation theory is that it gives the necessity part in the Nevanlinna-Pick interpolation theorem: given points z1, . . . , zn ∈ D and w1, . . . , wn ∈ C, there exists w ∈ S with w(zj) = wj for j = 1, . . . , n if and only if the associated Pick matrix ...
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We study certain sequences of rational functions with poles outside the unit circle. Such kind of sequences are recursively constructed based on sequences of complex numbers with norm less than one. In fact, such sequences are closely related to the Schur-Nevanlinna algorithm for Schur functions on the one hand and on the other hand to orthogonal rational functions on the unit circle. We shall ...
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Article history: Received 13 June 2013 Accepted 3 September 2015 Available online 19 January 2016 Communicated by L. Gross MSC: primary 49R05 secondary 47A56, 47A10
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ژورنال
عنوان ژورنال: Complex Analysis and Operator Theory
سال: 2006
ISSN: 1661-8254,1661-8262
DOI: 10.1007/s11785-006-0007-5