Interpolation theory in sectorial Stieltjes classes and explicit system solutions

被引:9
|
作者
Alpay, D
Tsekanovskii, E
机构
[1] Ben Gurion Univ Negev, Dept Math, IL-84105 Beer Sheva, Israel
[2] Niagara Univ, Dept Math, New York, NY 14109 USA
关键词
Stieltjes functions; sectorial operators; automorphisms of rational matrix-valued functions; interpolation;
D O I
10.1016/S0024-3795(00)00113-0
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We introduce sectorial classes of matrix-valued Stieltjes functions in which we solve the bi-tangential interpolation problem of Nudelman and Ball-Gohberg-Rodman. We consider also a new type of solutions of Nevanlinna-Pick interpolation problems, so-called explicit system solutions generated by Brodskii-Livsic colligations, and find conditions on interpolation data of their existence and uniqueness. We point out the connections between sectorial Stieltjes classes and sectorial operators, and find out new properties of the classical Nevanlinna-Pick interpolation matrices (in the scalar case). We present in terms of interpolation data the exact formula for the angle of sectoriality of the main operator in the explicit system solution as well as the criterion for this operator to be extremal. The interpolation model for nonselfadjoint matrices is established. (C) 2000 Elsevier Science Inc. All rights reserved.
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页码:91 / 136
页数:46
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