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Optimal polynomial approximants in Hp
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DOI：10.1016/j.jmaa.2025.130156.png)
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This work studies optimal polynomial approximants (OPAs) in the classical Hardy spaces on the unit disk, Hp (1 < p < infinity). In particular, we uncover some estimates concerning the OPAs of degree zero and one. It is also shown that if f is an element of Hp is an inner function, or if p > 2 is an even integer, then the roots of the nontrivial OPA for 1/fare bounded from the origin by a distance depending only on p. For p not equal 2, these results are made possible by the novel use of a family of inequalities which are derived from a Banach space analogue of the Pythagorean theorem.
Keyword:
Optimal polynomial approximant
Pythagorean inequality
期刊
J
IF:
1.2
论文数:
426
被引数:
0
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