Complete Nevanlinna–Pick kernels and the Schwarz lemma

Daniel Alpay; Tirthankar Bhattacharyya; Abhay Jindal; Poornendu Kumar

doi:10.1080/17476933.2025.2454683

Complete Nevanlinna–Pick kernels and the Schwarz lemma

Daniel Alpay
, Tirthankar Bhattacharyya
, Abhay Jindal
, Poornendu Kumar

Research output: Contribution to journal › Article › peer-review

Abstract

We prove a Schwarz lemma and Poincaré contractivity for functions in the unit ball of the multiplier algebra of a complete Nevanlinna-Pick reproducing kernel Hilbert space of holomorphic functions.

Original language	English
Pages (from-to)	2151-2165
Number of pages	15
Journal	Complex Variables and Elliptic Equations
Volume	70
Issue number	12
DOIs	https://doi.org/10.1080/17476933.2025.2454683
State	Published - 1 Jan 2025
Externally published	Yes

Keywords

Poincaré contractivity
Schur algorithm
Schwarz lemma
complete Nevanlinna Pick kernels
indefinite inner products
multiplier algebras

ASJC Scopus subject areas

Analysis
Numerical Analysis
Computational Mathematics
Applied Mathematics

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10.1080/17476933.2025.2454683

Cite this

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title = "Complete Nevanlinna–Pick kernels and the Schwarz lemma",

abstract = "We prove a Schwarz lemma and Poincar{\'e} contractivity for functions in the unit ball of the multiplier algebra of a complete Nevanlinna-Pick reproducing kernel Hilbert space of holomorphic functions.",

keywords = "Poincar{\'e} contractivity, Schur algorithm, Schwarz lemma, complete Nevanlinna Pick kernels, indefinite inner products, multiplier algebras",

author = "Daniel Alpay and Tirthankar Bhattacharyya and Abhay Jindal and Poornendu Kumar",

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AU - Alpay, Daniel

AU - Bhattacharyya, Tirthankar

AU - Jindal, Abhay

AU - Kumar, Poornendu

PY - 2025/1/1

Y1 - 2025/1/1

N2 - We prove a Schwarz lemma and Poincaré contractivity for functions in the unit ball of the multiplier algebra of a complete Nevanlinna-Pick reproducing kernel Hilbert space of holomorphic functions.

AB - We prove a Schwarz lemma and Poincaré contractivity for functions in the unit ball of the multiplier algebra of a complete Nevanlinna-Pick reproducing kernel Hilbert space of holomorphic functions.

KW - Poincaré contractivity

KW - Schur algorithm

KW - Schwarz lemma

KW - complete Nevanlinna Pick kernels

KW - indefinite inner products

KW - multiplier algebras

UR - https://www.scopus.com/pages/publications/85217834155

U2 - 10.1080/17476933.2025.2454683

DO - 10.1080/17476933.2025.2454683

M3 - Article

AN - SCOPUS:85217834155

SN - 1747-6933

VL - 70

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JO - Complex Variables and Elliptic Equations

JF - Complex Variables and Elliptic Equations

IS - 12

ER -

Complete Nevanlinna–Pick kernels and the Schwarz lemma

Abstract

Keywords

ASJC Scopus subject areas

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