On a multi-point interpolation problem for generalized Schur functions

The Schur problem and block operator CMV matrices

The CMV matrices and their sub-matrices are applied to the description of all solutions to the Schur interpolation problem for contractive analytic operator-valued functions in the unit disk (the Schur class functions).

菱形格点上的Schur函数

Schur functions on a rhombic lattice

本文通过定义合适的移位算子，将离散解析Schur函数的研究扩展到菱形格点，并应用于加权Hardy空间中的基本插值问题，引入了Blaschke因子的离散对应物。

稳定系统中的振幅最大化、Schur正性及多项式插值的若干猜想

Amplitude maximization in stable systems, Schur positivity, and some conjectures on polynomial interpolation

针对稳定系统中齐次线性差分方程解的振幅最大化问题，通过将其约化为单项式插值问题并结合对称函数与Schur正性理论，证明最大值在边界重根处取得，还提出了实整函数导数估计中单项式极值性的猜想。

Boundary Nevanlinna-Pick interpolation via reduction and augmentation

We give an elementary proof of Sarason's solvability criterion for the Nevanlinna-Pick problem with boundary interpolation nodes and boundary target values. We also give a concrete parametrization of all solutions of such a problem. The proofs are based on a reduction method due to Julia and Nevanlinna. Reduction of functions corresponds to Schur complementation of the corresponding Pick matrices.

四面块上的函数论：实现、插值、延拓与Toeplitz corona定理

Function Theory on Tetrablock: Realization, Interpolation, Extension and Toeplitz Corona Theorem

本文在四面块上引入Schur-Agler型函数类，建立实现定理，并给出插值定理、延拓定理与Toeplitz corona定理的四面块版本。

无穷多变量下的Schur-Agler类

The Schur-Agler class in infinitely many variables

本文定义了无穷多变量下的Schur-Agler类，证明了Agler分解的推广及传递函数实现，给出了Pick插值型定理，并探讨了其与Dirichlet级数的联系。

五角块的实现、插值、扩展及其在 $\mathbb D^2$、$\mathbb G_2$ 上的应用

Realization, interpolation, extension on the pentablock and applications to $\mathbb D^2$, $\mathbb G_2$

本文为五角块 $\mathbb P$ 引入 Schur-Agler 类，建立实现定理、插值定理和扩展定理，并应用于双圆盘 $\mathbb D^2$ 和对称双圆盘 $\mathbb G_2$，给出新的刻画和替代证明。

Boundary Nevanlinna-Pick interpolation for generalized Nevanlinna functions

We formulate three boundary Nevanlinna-Pick interpolation problems for generalized Nevanlinna functions. For each problem, we parameterize the set of all solutions in terms of a linear fractional transformation with an extended Nevanlinna class parameter.

Generalized quaternionic Schur functions in the ball and half-space and Krein-Langer factorization

In this paper we prove a new version of Krein-Langer factorization theorem in the slice hyperholomorphic setting which is more general than the one proved in [D. Alpay, F. Colombo, I. Sabadini, Krein-Langer factorization and related topics in the slice hyperholomorphic setting, J. Geom. Anal., 24 (2014), 843--872]. We treat both the case of functions with $κ$ negative squares defined on subsets of the quaternionic unit ball or on subsets of the half space of quaternions with positive real part. A crucial tool in the proof of our results is the Schauder-Tychonoff theorem and an invariant subspa…

A rich structure related to the construction of analytic matrix functions

We analyse two special cases of $μ$-synthesis problems which can be reduced to interpolation problems in the set of analytic functions from the disc into the symmetrised bidisc and into the tetrablock. For these inhomogeneous domains we study the structure of interconnections between the set of analytic functions from the disc into the given domain, the matricial Schur class, the Schur class of the bidisc, and the set of pairs of positive kernels on the bidisc subject to a boundedness condition. We use the theories of Hilbert function spaces and of reproducing kernels to establish these connec…

Interpolation without commutants

We introduce a "dual-space approach" to mixed Nevanlinna-Pick/Carathéodory-Schur interpolation in Banach spaces X of holomorphic functions on the disk. Our approach can be viewed as complementary to the well-known commutant lifting approach of D. Sarason and B. Nagy-C.Foiaş. We compute the norm of the minimal interpolant in X by a version of the Hahn-Banach theorem, which we use to extend functionals defined on a subspace of kernels without increasing their norm. This Functional extensions lemma plays a similar role as Sarason's Commutant lifting theorem but it only involves the predual of X a…

对称多圆盘的函数论性质及其推广

Function theoretic aspects of the symmetrized polydisc and generalization

本文研究对称多圆盘$\boldsymbol{\reals^d}$的函数论性质，引入Schur-Agler型类并建立相关定理，还将这些结果推广至更一般的对称域族$\boldsymbol{\theta_d}$。

Analytic functions on the bidisk at boundary singularities via Hilbert space methods

We investigate the behavior of a generalized Hilbert space model of a function in the Schur class of the bidisk at singular boundary points that satisfy a growth condition. We examine the relationship between the boundary behavior of Schur functions and the geometry of corresponding generalized Hilbert space models. We describe a geometric condition on an associated operator that classifies the behavior of the directional derivative of the underlying Schur function at a carapoint.