The Structure of Inner Multipliers on Spaces with Complete Nevanlinna Pick Kernels

Nevanlinna-Pick problem and uniqueness of left inverses in convex domains, symmetrized bidisc and tetrablock

In the paper we discuss the problem of uniqueness of left inverses (solutions of two point Nevanlinna-Pick problem) in bounded convex domains, strongly linearly convex domains, the symmetrized bidisc and the tetrablock.

Gelfand transforms and boundary representations of complete Nevanlinna--Pick quotients

The main objects under study are quotients of multiplier algebras of certain complete Nevanlinna--Pick spaces, examples of which include the Drury--Arveson space on the ball and the Dirichlet space on the disc. We are particularly interested in the non-commutative Choquet boundaries for these quotients. Arveson's notion of hyperrigidity is shown to be detectable through the essential normality of some natural multiplication operators, thus extending previously known results on the Arveson--Douglas conjecture. We also highlight how the non-commutative Choquet boundaries of these quotients are i…

Self-mappings of the quaternionic unit ball: multiplier properties, Schwarz-Pick inequality, and Nevanlinna--Pick interpolation problem

We study several aspects concerning slice regular functions mapping the quaternionic open unit ball into itself. We characterize these functions in terms of their Taylor coefficients at the origin and identify them as contractive multipliers of the Hardy space. In addition, we formulate and solve the Nevanlinna-Pick interpolation problem in the class of such functions presenting necessary and sufficient conditions for the existence and for the uniqueness of a solution. Finally, we describe all solutions to the problem in the indeterminate case.

Nevanlinna-Pick interpolation for $C+BH^\infty$

Given an inner function $B$ we classify the invariant subspaces of the algebra $H^\infty_B:=\mathbb{C}+BH^\infty$. We derive a formula in terms of these invariant subspaces for the distance of an element in $L^\infty$ to a certain weak*-closed ideal in $H^\infty_B$ and use this to prove an analogue of the Nevanlinna-Pick interpolation theorem.

A Beurling-Lax-Halmos theorem for spaces with a complete Nevanlinna-Pick factor

We provide a short argument to establish a Beurling-Lax-Halmos theorem for reproducing kernel Hilbert spaces whose kernel has a complete Nevanlinna-Pick factor. We also record factorization results for pairs of nested invariant subspaces.

Complete Nevanlinna-Pick kernels

We give a new treatment of Quiggin's and McCullough's characterization of complete Nevanlinna-Pick kernels. We show that a kernel has the matrix-valued Nevanlinna-Pick property if and only if it has the vector-valued Nevanlinna-Pick property. We give a representation of all complete Nevanlinna-Pick kernels, and show that they are all restrictions of a universal complete Nevanlinna-Pick kernel.

Hilbert function spaces and the Nevanlinna-Pick problem on the polydisc

In the paper `Distinguished Varieties,' Agler and McCarthy used Hilbert function spaces to study the uniqueness properties of the Nevanlinna-Pick problem on the bidisc. In this work we give a geometric procedure for constructing a Nevanlinna-Pick problems on D^n with a specified set of uniqueness. On the way to establishing this procedure, we prove a result about Hilbert function spaces and partially answer a question posed by Agler and McCarthy.

容许Hardy型完备Nevanlinna-Pick空间的复结构

Complex structure that admits complete Nevanlinna-Pick spaces of Hardy type

本文刻画了不可约完备Nevanlinna-Pick空间乘子范数与上确界范数相等的集合，并证明Hardy型该空间的既约复空间必双全纯同构于去掉零解析容量集的单位圆盘，从而确立Hardy空间的唯一性。

A constrained Nevanlinna-Pick interpolation problem for matrix-valued functions

Recent results of Davidson-Paulsen-Raghupathi-Singh give necessary and sufficient conditions for the existence of a solution to the Nevanlinna-Pick interpolation problem on the unit disk with the additional restriction that the interpolant should have the value of its derivative at the origin equal to zero. This concrete mild generalization of the classical problem is prototypical of a number of other generalized Nevanlinna-Pick interpolation problems which have appeared in the literature (for example, on a finitely-connected planar domain or on the polydisk). We extend the results of Davidson…

Which de Branges-Rovnyak spaces have complete Nevanlinna-Pick property?

We characterize the de Branges-Rovnyak spaces with complete Nevanlinna-Pick property. Our method relies on the general theory of reproducing kernel Hilbert spaces.

On the isomorphism problem for multiplier algebras of Nevanlinna-Pick spaces

We continue the investigation of the isomorphism problem for multiplier algebras of reproducing kernel Hilbert spaces with the complete Nevanlinna-Pick property. In contrast to previous work in this area, we do not study these spaces by identifying them with restrictions of a universal space, namely the Drury-Arveson space. Instead, we work directly with the Hilbert spaces and their reproducing kernels. In particular, we show that two multiplier algebras of Nevanlinna-Pick spaces on the same set are equal if and only if the Hilbert spaces are equal. Most of the article is devoted to the study …

Spectral Nevanlinna-Pick problem and weak extremals in the symmetrized bidisc

The main goal of the paper is to study $m$-extremal mappings in the symmetrized bidisc showing that they are rational and $\GG_2$-inner which, in particular, answers a question posed in \cite{Agl-Lyk-You 2013}.

Nevanlinna-Pick spaces with hyponormal multiplication operators

We show that the Hardy space on the unit disk is the only non-trivial irreducible reproducing kernel Hilbert space which satisfies the complete Nevanlinna-Pick property and hyponormality of all multiplication operators.

Three-point Nevanlinna Pick problem in the polydisc

It is very elementary to observe that functions interpolating an extremal two-point Pick problem on the polydisc are just left inverses to complex geodesics. In the present article we show that the same property holds for a three-point Pick problem on polydiscs, i.e. it may be expressed it in terms of three-complex geodesics. Using this idea we are able to solve that problem obtaining formulas and a uniqueness theorem for solutions of extremal problems. In particular, we determine a class of rational inner functions interpolating that problem. Possible extensions and further investigations are…

Nonisotropically balanced domains, Lempert function estimates, and the spectral Nevanlinna-Pick problem

We introduce the notion of a λ-nonisotropically balanced domain and show that the symmetrized polydisc in C^n, n \geq 2, is an example of such a domain. Given a λ-nonisotropically balanced domain Ω, we derive effective estimates from above and from below for the Lempert function at (0,z)\inΩ\timesΩ. We use these estimates to derive certain conditions for realising a two-point Nevanlinna-Pick interpolation in the symmetrized polydisc. Applying the ideas used in the derivation of our Lempert function estimates to the so-called spectral unit ball Ω_n, we deduce: a) a formula for the Lempert funct…

Nevanlinna-Pick Interpolation and Factorization of Linear Functionals

If $\fA$ is a unital weak-$*$ closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property $\bA_1(1)$, then the cyclic invariant subspaces index a Nevanlinna-Pick family of kernels. This yields an NP interpolation theorem for a wide class of algebras. In particular, it applies to many function spaces over the unit disk including Bergman space. We also show that the multiplier algebra of a complete NP space has $\bA_1(1)$, and thus this result applies to all of its subalgebras. A matrix version of this result is also established. It applies, in particu…

The Nevanlinna-Pick matrix interpolation in the Carathéodory class with infinite data both in the nondegenerate and degenerate cases

In this paper we study the Nevanlinna-Pick matrix interpolation problem in the Carathéodory class with infinite data (both in the nondegenerate and degenerate cases). We develop the Szökefalvi-Nagy and Korányi operator approach to obtain an analytic description of all solutions of the problem. Simple necessary and sufficient conditions for the determinacy of the problem are given.

The Toeplitz corona problem for algebras of multipliers on a Nevanlinna-Pick space

Suppose $\fA$ is an algebra of operators on a Hilbert space $H$ and $A_1,..., A_n \in \fA$. If the row operator $[A_1,..., A_n] \in B(H^{(n)},H)$ has a right inverse in $B(H, H^{(n)})$, the Toeplitz corona problem for $\fA$ asks if a right inverse can be found with entries in $\fA$. When $H$ is a complete Nevanlinna-Pick space and $\fA$ is a weakly-closed algebra of multiplication operators on $H$, we show that under a stronger hypothesis, the corona problem for $\fA$ has a solution. When $\fA$ is the full multiplier algebra of $H$, the Toeplitz corona theorems of Arveson, Schubert and Ball-Tr…

Factorizations induced by complete Nevanlinna-Pick factors

We prove a factorization theorem for reproducing kernel Hilbert spaces whose kernel has a normalized complete Nevanlinna-Pick factor. This result relates the functions in the original space to pointwise multipliers determined by the Nevanlinna-Pick kernel and has a number of interesting applications. For example, for a large class of spaces including Dirichlet and Drury-Arveson spaces, we construct for every function $f$ in the space a pluriharmonic majorant of $|f|^2$ with the property that whenever the majorant is bounded, the corresponding function $f$ is a pointwise multiplier.

Nevanlinna-Pick Interpolation On Certain Subalgebras of $H^{\infty}(\mathbb{D})$

Given a collection $K$ of positive integers, let $H^{\infty}_K(\mathbb{D})$ denote the set of all bounded analytic functions defined on the unit disk $\mathbb{D}$ in $\mathbb{C}$ whose $k^{\text{th}}$ derivative vanishes at zero, for all $k \in K$. In this paper, we establish a Nevanlinna-Pick interpolation result for the subalgebra $H^{\infty}_K(\mathbb{D})$, where $K = \{1,2,\dotsc,k\}$, which is a slight generalization of the interpolation theorem that Davidson, Paulsen, Raghupathi, and Singh proved for the algebra $H^{\infty}_{\{1\}}(\mathbb{D})$. Furthermore, we provide a sufficient condi…

Effective noncommutative Nevanlinna-Pick interpolation in the row ball, and applications

We provide an effective single-matrix criterion, in terms of what we call the elementary Pick matrix, for the solvability of the noncommutative Nevanlinna-Pick interpolation problem in the row ball, and provide some applications. In particular we show that the so-called "column-row property" fails for the free semigroup algebras, in stark contrast to the analogous commutative case. Additional applications of the elementary Pick matrix include a local dilation theorem for matrix row contractions and interpolating sequences in the noncommutative setting. Finally we present some numerical results…

动态Nevanlinna-Pick理论、协变伸缩与非交换簇

Dynamic Nevanlinna-Pick Theory, Covariance Dilations, and Non-commutative Varieties

该研究推广了Nevanlinna-Pick插值理论，建立了相关算子理论框架，证明了H^∞(𝔻)成员关系的普遍检测方法，并揭示非交换内簇上Arveson型完全谱集表示失效的特性。

Nevanlinna-Pick Kernels and Localization

We describe those reproducing kernel Hilbert spaces of holomorphic functions on domains in ${\Bbb C}^d$ for which an analogue of the Nevanlinna-Pick theorem holds, in other words when the existence of a (possibly matrix-valued) function in the unit ball of the multiplier algebra with specified values on a finite set of points is equivalent to the positvity of a related matrix. Our description is in terms of a certain localization property of the kernel.

Nevanlinna-Pick interpolation on distinguished varieties in the bidisk

This article treats Nevanlinna-Pick interpolation in the setting of a special class of algebraic curves called distinguished varieties. An interpolation theorem, along with additional operator theoretic results, is given using a family of reproducing kernels naturally associated to the variety. The examples of the Neil parabola and doubly connected domains are discussed.

Multivariable operator-valued Nevanlinna-Pick interpolation: a survey

The theory of Nevanlinna-Pick and Carathéodory-Fejér interpolation for matrix- and operator-valued Schur class functions on the unit disk is now well established. Recent work has produced extensions of the theory to a variety of multivariable settings, including the ball and the polydisk (both commutative and noncommutative versions), as well as a time-varying analogue. Largely independent of this is the recent Nevanlinna-Pick interpolation theorem by P.S. Muhly and B. Solel for an abstract Hardy algebra set in the context of a Fock space built from a $W^*$-correspondence E over a $W^{*}$-alge…

特征簇与对称双圆盘上的 Nevanlinna-Pick 插值问题

Distinguished varieties and the Nevanlinna-Pick interpolation problem on the symmetrized bidisk

本文研究对称双圆盘上可解 Nevanlinna-Pick 插值问题的唯一性集合，证明其为由插值数据规范构造的唯一性簇，并给出其中特征簇的完整代数与几何刻画。

Robust control, multidimensional systems and multivariable Nevanlinna-Pick interpolation

The connection between the standard $H^\infty$-problem in control theory and Nevanlinna-Pick interpolation in operator theory was established in the 1980s, and has led to a fruitful cross-pollination between the two fields since. In the meantime, research in $H^\infty$-control theory has moved on to the study of robust control for systems with structured uncertainties and to various types of multidimensional systems, while Nevanlinna-Pick interpolation theory has moved on independently to a variety of multivariable settings. Here we review these developments and indicate the precise connection…

右半平面中的 Nevanlinna-Pick 插值

Nevanlinna-Pick interpolation in the right half-plane

本文研究右半平面上的 Nevanlinna-Pick 插值，证明 Szegö-Dirichlet 核的正整数次幂均无两点标量 Pick 性质，并给出 $\mathbb H_0$ 的网络实现公式。

Complete Nevanlinna-Pick kernels And The Characteristic Function

This note finds a new characterization of complete Nevanlinna-Pick kernels on the Euclidean unit ball. The classical theory of Sz.-Nagy and Foias about the characteristic function is extended in this note to a commuting tuple $\bfT$ of bounded operators satisfying the natural positivity condition of $1/k$-contractivity for an irreducible unitarily invariant complete Nevanlinna-Pick kernel. The characteristic function is a multiplier from $H_k \otimes \cE$ to $H_k \otimes \cF$, {\em factoring} a certain positive operator, for suitable Hilbert spaces $\cE$ and $\cF$ depending on $\bfT$. There is…

完全 Nevanlinna-Pick 核、Schwarz 引理与 Schur 算法

Complete Nevanlinna-Pick kernels, the Schwarz lemma and the Schur algorithm

本文研究满足完全 Nevanlinna-Pick 性质的再生核 Hilbert 空间中乘子代数单位球元素的 Schwarz 引理、Schur 算法及 Poincaré 压缩性。

All solutions to an operator Nevanlinna-Pick interpolation problem

The main results presented in this paper provide a complete and explicit description of all solutions to the left tangential operator Nevanlinna- Pick interpolation problem assuming the associated Pick operator is strictly positive. The complexity of the solutions is similar to that found in descriptions of the sub-optimal Nehari problem and variation on the Nevanlinna-Pick interpolation problem in the Wiener class that have been obtained through the band method. The main techniques used to derive the formulas are based on the theory of co-isometric realizations, and use the Douglas factorizat…

具有完全Nevanlinna-Pick因子的核与特征函数

Kernels with complete Nevanlinna-Pick factors and the characteristic function

本文提出统一框架，为具有完全Nevanlinna-Pick因子的核构造特征函数，涵盖并泛化已有结果，并阐明Drury-Arveson核的天然适用性。

Convex invertible cones and Nevanlinna-Pick interpolation: The suboptimal case

Nevanlinna-Pick interpolation developed from a topic in classical complex analysis to a useful tool for solving various problems in control theory and electrical engineering. Over the years many extensions of the original problem were considered, including extensions to different function spaces, nonstationary problems, several variable settings and interpolation with matrix and operator points. Here we discuss a variation on Nevanlinna-Pick interpolation for positive real odd functions evaluated in real matrix points. This problem was studied by Cohen and Lewkowicz using convex invertible con…

Free Pick functions: representations, asymptotic behavior and matrix monotonicity in several noncommuting variables

We extend the study of the Pick class, the set of complex analytic functions taking the upper half plane into itself, to the noncommutative setting. R. Nevanlinna showed that elements of the Pick class have certain integral representations which reflect their asymptotic behavior at infinity. Loewner connected the Pick class to matrix monotone functions. We generalize the Nevanlinna representation theorems and Loewner's theorem on matrix monotone functions to the free Pick class, the collection of functions that map tuples of matrices with positive imaginary part into the matrices with positive…

$\mathbb K$-不变再生核的完整Nevanlinna-Pick性质

Complete Nevanlinna-Pick property of $\mathbb K$-Invariant Reproducing Kernels

本文研究了$\mathbb K$-不变再生核的完整Nevanlinna-Pick性质，通过扩展特征函数概念并构造显式特征函数，给出了具有该性质的核的特征化条件。

de Branges-Rovnyak 空间中的完全 Nevanlinna-Pick 空间

de Branges-Rovnyak spaces which are complete Nevanlinna-Pick spaces

本文刻画了 de Branges-Rovnyak 空间为完全 Nevanlinna-Pick 空间的条件，推广了 Hardy 空间和 Drury-Arveson 空间的已有结果，并证明双圆盘或单位圆盘情形仅当等距同构于 Hardy 空间时成立，而 $n\ge 3$ 时永不成立。

单项式簇上完全Pick代数的等距刚性

Isometric rigidity of complete Pick algebras on monomial varieties

该研究针对有限维单位球中的单项式簇建立几何刚性定理，推导得到完全Nevanlinna-Pick狄利克雷级数核乘子代数及有界Reinhardt域上相关核的等距分类结果。

完全Nevanlinna-Pick核与曲率不变量

Complete Nevanlinna-Pick Kernels and the Curvature Invariant

该文研究酉不变完全Nevanlinna-Pick核下满足压缩性条件的交换d元有界算子组的曲率不变量，给出其渐近公式，在纯算子情形证明其为整数，并探究其与纤维维数的联系及特征函数为多项式时的简化公式。

Nevanlinna-Pick norms: 向 commutative Banach algebras 谱的 scattered-Cantor 分歧论迈进

Nevanlinna--Pick norms on scattered and Cantor spectra

本文研究了Nevanlinna-Pick norms在交换半单Banach代数中的性质，证明了当谱为紧散集时，代数是C(K)的等距同构，且讨论了统一代数中Gleason部分为单点的情况。

On the isomorphism question for complete Pick multiplier algebras

Every multiplier algebra of an irreducible complete Pick kernel arises as the restriction algebra $\mv = \{f\big|_V : f \in \cM_d\}$, where $d$ is some integer or $\infty$, $\cM_d$ is the multiplier algebra of the Drury-Arveson space $H^2_d$, and $V$ is a subvariety of the unit ball. For finite $d$ it is known that, under mild assumptions, every isomorphism between two such algebras $\mv$ and $\mw$ is induced by a biholomorphism between $W$ and $V$. In this paper we consider the converse, and obtain positive results in two directions. The first deals with the case where $V$ is the proper image…

On the Nevanlinna problem - Characterization of all Schur-Agler class solutions

Given a domain $Ω$ in $\mathbb{C}^m$, and a finite set of points $z_1,\ldots, z_n\in Ω$ and $w_1,\ldots, w_n\in \mathbb{D}$ (the open unit disc in the complex plane), the $Pick\, interpolation\, problem$ asks when there is a holomorphic function $f:Ω\rightarrow \overline{\mathbb{D}}$ such that $f(z_i)=w_i,1\leq i\leq n$. Pick gave a condition on the data $\{z_i, w_i:1\leq i\leq n\}$ for such an $interpolant$ to exist if $Ω=\mathbb{D}$. Nevanlinna characterized all possible functions $f$ that $interpolate$ the data. We generalize Nevanlinna's result to an arbitrary set $Ω$. In this case, the fu…

Every complete Pick space satisfies the column-row property

In the theory of complete Pick spaces, the column-row property has appeared in a variety of contexts. We show that it is satisfied by every complete Pick space in the following strong form: each sequence of multipliers that induces a contractive column multiplication operator also induces a contractive row multiplication operator. In combination with known results, this yields a number of consequences. Firstly, we obtain multiple applications to the theory of weak product spaces, including factorization, multipliers and invariant subspaces. Secondly, there is a short proof of the characterizat…

Cauchy transforms arising from homomorphic conditional expectations parametrize free Pick functions but those arising from conditional expectations do not

Nevanlinna showed that Cauchy transforms of probability measures parametrize all functions from the upper half plane into itself satisfying a certain asymptotic condition at infinity. We show that the correspondence fails in general for the unbounded case for somewhat trivial reasons; however, we show that in a setting of "homomorphic" operator valued free probability that Cauchy transforms of homomorphic conditional expectations parametrize free Pick functions.

Multiplier tests and subhomogeneity of multiplier algebras

Multipliers of reproducing kernel Hilbert spaces can be characterized in terms of positivity of $n \times n$ matrices analogous to the classical Pick matrix. We study for which reproducing kernel Hilbert spaces it suffices to consider matrices of bounded size $n$. We connect this problem to the notion of subhomogeneity of non-selfadjoint operator algebras. Our main results show that multiplier algebras of many Hilbert spaces of analytic functions, such as the Dirichlet space and the Drury-Arveson space, are not subhomogeneous, and hence one has to test Pick matrices of arbitrarily large matrix…

非交换交换子提升、插值与移位不变子空间

Noncommutative commutant lifting, interpolation, and shift-invariant subspaces

本文在非交换Drury-Arveson空间中建立Sarason型交换子提升定理，解决非交换Nevanlinna-Pick插值问题，并给出移位不变子空间的Beurling-Lax-Halmos型刻画。

Unbounded multipliers of complete Pick spaces

We examine densely defined (but possibly unbounded) multiplication operators in Hilbert function spaces possessing a complete Nevanlinna-Pick (CNP) kernel. For such a densely defined operator $T$, the domains of $T$ and $T^*$ are reproducing kernel Hilbert spaces contractively contained in the ambient space. We study several aspects of these spaces, especially the domain of $T^*$, which can be viewed as analogs of the classical deBranges-Rovnyak spaces in the unit disk.

完全Pick代数的同构问题：综述

The isomorphism problem for complete Pick algebras: a survey

本综述围绕完全Pick代数的同构问题展开，阐述其作为满足Pick插值定理的乘子代数的研究背景，介绍其通过Drury-Arveson空间乘子限制到单位球子簇的具体实现形式，总结基于复几何分类该代数的相关研究，描述所用工具方法并澄清修正文献内容。

具有完全Pick性质的狄利克雷级数空间

Spaces of Dirichlet series with the complete Pick property

本文刻画了核为$k(s,u) = \sum a_n n^{-s-\bar u}$形式的狄利克雷级数再生核希尔伯特空间何时为完全Pick空间，引入弱同构概念并证明多类此类空间与Drury-Arveson空间$H^2_d$弱同构，揭示其乘子代数性质。

A Hill-Pick matrix criteria for the Lyapunov order

The Lyapunov order appeared in the study of Nevanlinna-Pick interpolation for positive real odd functions with general (real) matrix points. For real or complex matrices $A$ and $B$ it is said that $B$ Lyapunov dominates $A$ if \begin{equation*} H=H^*,\quad HA+A^*H \geq 0 \quad \implies \quad HB+B^*H \geq 0. \end{equation*} (In case $A$ and $B$ are real we usually restrict to real Hermitian matrices $H$, i.e., symmetric $H$.) Hence $B$ Lyapunov dominates $A$ if all Lyapunov solutions of $A$ are also Lyapunov solutions of $B$. In this chapter we restrict to the case that appears in the study of…

Multipliers and operator space structure of weak product spaces

In the theory of reproducing kernel Hilbert spaces, weak product spaces generalize the notion of the Hardy space $H^1$. For complete Nevanlinna-Pick spaces $\mathcal H$, we characterize all multipliers of the weak product space $\mathcal H \odot \mathcal H$. In particular, we show that if $\mathcal H$ has the so-called column-row property, then the multipliers of $\mathcal H$ and of $\mathcal H \odot \mathcal H$ coincide. This result applies in particular to the classical Dirichlet space and to the Drury-Arveson space on a finite dimensional ball. As a key device, we exhibit a natural operator…

The Smirnov class for spaces with the complete Pick property

We show that every function in a reproducing kernel Hilbert space with a normalized complete Pick kernel is the quotient of a multiplier and a cyclic multiplier. This extends a theorem of Alpay, Bolotnikov and Kaptanoğlu. We explore various consequences of this result regarding zero sets, spaces on compact sets and Gleason parts. In particular, using a construction of Salas, we exhibit a rotationally invariant complete Pick space of analytic functions on the unit disc for which the corona theorem fails.

关于Nevanlinna问题——与给定核相关联的所有Schur-Agler类解的刻画

On the Nevanlinna problem -- Characterization of all Schur-Agler class solutions affiliated with a given kernel

本文将Nevanlinna关于插值问题的结果推广至多维复数域，刻画了与给定完全正核相关联的Schur-Agler类全纯插值函数，并验证了该理论在双圆盘、对称双圆盘和圆环上的成功应用。

完全Pick空间中的简单插值序列

Simply interpolating sequences in complete Pick spaces

本文刻画了完全Pick空间的简单插值序列，证明其等价于强分离序列，回答了Agler和McCarthy的问题，并揭示了在加权Dirichlet空间等例子中简单插值不蕴含乘子插值。

乘子品种和乘子代数的CNP狄利克雷级数核

Multiplier varieties and multiplier algebras of CNP Dirichlet series kernels

研究CNP狄利克雷级数核的乘子代数等距和代数同构问题，通过多项式方程确定乘子品种，从而分类其同构性，并解决McCarthy和Shalit提出的问题。