| Autor: |
Arora, Palak, Augat, Meric, Jury, Michael T., Sargent, Meredith |
| Předmět: |
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| Zdroj: |
Proceedings of the American Mathematical Society; Feb2024, Vol. 152 Issue 2, p455-470, 16p |
| Abstrakt: |
Motivated by recent work on optimal approximation by polynomials in the unit disk, we consider the following noncommutative approximation problem: for a polynomial f in d freely noncommuting arguments, find a free polynomial p_n, of degree at most n, to minimize c_n ≔\|p_nf-1\|^2. (Here the norm is the \ell ^2 norm on coefficients.) We show that c_n\to 0 if and only if f is nonsingular in a certain nc domain (the row ball), and prove quantitative bounds. As an application, we obtain a new proof of the characterization of polynomials cyclic for the d-shift. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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