A polynomial approximation result for free Herglotz-Agler functions
Kenta Kojin
TL;DR
This paper establishes a noncommutative Schwarz lemma for the nc Schur-Agler class, characterizes free Herglotz functions, and demonstrates their approximation by free polynomials, advancing understanding in noncommutative function theory.
Contribution
It introduces a noncommutative Schwarz lemma, characterizes free Herglotz functions, and proves their approximation by free polynomials, providing new tools in noncommutative analysis.
Findings
Noncommutative Schwarz lemma for nc Schur-Agler class
Homeomorphism between nc Schur-Agler and free Herglotz classes
Approximation of free Herglotz functions by free polynomials
Abstract
In this paper, we prove a noncommutative (nc for short) analog of Schwarz lemma for the nc Schur-Agler class and prove that the regular nc Schur-Agler class and the regular free Herglotz class are homeomorphic. Moreover, we give a characterization of regular free Herglotz functions. As an application, we will show that any regular free Herglotz functions can uniformly be approximated by regular Herglotz free polynomials.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHolomorphic and Operator Theory · Spectral Theory in Mathematical Physics · Advanced Topics in Algebra