Journal of Operator Theory

Volume 94, Issue 1, Summer 2025 pp. 271-289.

Kernels with complete Nevanlinna-Pick factors and the characteristic function

Authors: Tirthankar Bhattacharyya (1), Abhay Jindal (2)
Author institution: (1) Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India
(2) Department of Mathematics, Indian Institute of Science, Bangalore, 560012, India

Summary: We present a unified framework for deriving characteristic functions for kernels that allow a complete Nevanlinna-Pick factor. Notably, our approach not only encapsulates all previously documented cases but also achieves a generalization, thereby expanding the concept of the characteristic function substantially. We also provide an explanation for the prominence of the Drury-Arveson kernel in all previously established results by showing that the Drury-Arveson kernel was the natural choice inherently suitable for those situations.

DOI: http://dx.doi.org/10.7900/jot.2023dec09.2445
Keywords: complete Nevanlinna-Pick kernels, Dirichlet kernel, Drury-Arveson kernel, characteristic function

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