$$\varvec{q}$$有理函数和内插法与完全Nevanlinna-Pick核

IF 0.8 3区数学 Q2 MATHEMATICS Integral Equations and Operator Theory Pub Date : 2024-09-14 DOI:10.1007/s00020-024-02779-2

Daniel Alpay, Paula Cerejeiras, Uwe Kaehler, Baruch Schneider

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引用次数: 0

摘要

本文介绍了矩阵值 q 有理函数的概念。与经典情况相比，我们给出了不同的特征，主要强调实化，并讨论了代数操作。我们还在 q 变形重现核希尔伯特空间的背景下研究了舒尔乘法器和完全内万林纳-皮克核的概念，并在使用舒尔乘法器和完全内万林纳-皮克核的插值问题方面提供了首次应用。

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$$\varvec{q}$$ -rational Functions and Interpolation with Complete Nevanlinna–Pick Kernels

In this paper we introduce the concept of matrix-valued q-rational functions. In comparison to the classical case, we give different characterizations with principal emphasis on realizations and discuss algebraic manipulations. We also study the concept of Schur multipliers and complete Nevanlinna–Pick kernels in the context of q-deformed reproducing kernel Hilbert spaces and provide first applications in terms of an interpolation problem using Schur multipliers and complete Nevanlinna–Pick kernels.

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来源期刊

Integral Equations and Operator Theory 数学-数学

CiteScore

1.60

自引率

0.00%

发文量

审稿时长

6 months

期刊介绍： Integral Equations and Operator Theory (IEOT) is devoted to the publication of current research in integral equations, operator theory and related topics with emphasis on the linear aspects of the theory. The journal reports on the full scope of current developments from abstract theory to numerical methods and applications to analysis, physics, mechanics, engineering and others. The journal consists of two sections: a main section consisting of refereed papers and a second consisting of short announcements of important results, open problems, information, etc.