q-rational Functions and Interpolation withComplete Nevanlinna-Pick Kernels

被引：0

作者：

Alpay, Daniel ^{[1
]}

Cerejeiras, Paula ^{[2
]}

Kaehler, Uwe ^{[2
]}

Schneider, Baruch ^{[3
]}

机构：

[1] Chapman Univ, Schmid Coll Sci & Technol, Fac Math Phys & Computat, One Univ Dr, Orange, CA 92866 USA

[2] Univ Aveiro, Ctr Res & Dev Math & Applicat, Dept Math, Campus Univ Santiago, P-3810193 Aveiro, Portugal

[3] Univ Ostrava, Dept Math, 30 Dubna 22, Ostrava 70200, Czech Republic

来源：

INTEGRAL EQUATIONS AND OPERATOR THEORY | 2024年 / 96卷 / 04期

关键词：

Rational functions; q-Calculus; Jordan chains; CNP kernels; Schur multipliers; HILBERT-SPACES; REALIZATION; PRODUCTS; HARDY;

D O I：

10.1007/s00020-024-02779-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：37

共 39 条

[1]

Agler J, 2002, Grad. Stud. Math., V44

[2] Gleason's problem and homogeneous interpolation in Hardy and Dirichlet-type spaces of the ball [J].

Alpay, D ;

Kaptanoglu, HT .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 276 (02) :654-672

[3] The Schur algorithm and reproducing kernel Hilbert spaces in the ball [J].

Alpay, D ;

Bolotnikov, V ;

Kaptanoglu, HT .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2002, 342 :163-186

[4]

Alpay D, 1996, LINEAR ALGEBRA APPL, V243, P3

[5]

Alpay D., 2001, SCHUR ALGORITHM REPR

[6]

Alpay D., 2024, Exercises in Applied Mathematics: With a View Toward Information Theory, Machine Learning, Wavelets and Statistical Physics, DOI [10.1007/978-3-031-51822-5, DOI 10.1007/978-3-031-51822-5]

[7] GENERALIZED q-FOCK SPACES AND STRUCTURAL IDENTITIES [J].