1. CMB Online first
||Remarks on inner functions and optimal approximants|
We discuss the concept of inner function in reproducing kernel Hilbert spaces with an orthogonal basis of monomials and examine connections between inner functions and optimal polynomial approximants to $1/f$, where $f$ is a function in the space. We revisit some classical examples from this perspective, and show how a construction of Shapiro and Shields can be modified to produce inner functions.
Keywords:inner function, reproducing Kernel Hilbert Space, operator-theoretic function theory
2. CMB 2008 (vol 51 pp. 481)
||Universal Inner Functions on the Ball |
It is shown that given any sequence of automorphisms $(\phi_k)_k$ of the
unit ball $\bn$ of $\cn$ such that $\|\phi_k(0)\|$ tends to $1$,
there exists an inner function
$I$ such that the family of ``non-Euclidean translates"
$(I\circ\phi_k)_k$ is locally uniformly dense in the unit ball of
Keywords:inner functions, automorphisms of the ball, universality
Categories:32A35, 30D50, 47B38
3. CMB 2005 (vol 48 pp. 409)