location:  Publications → journals
Search results

Search: All articles in the CMB digital archive with keyword inner function

 Expand all        Collapse all Results 1 - 3 of 3

1. CMB Online first

Bénéteau, Catherine Anne; Fleeman, Matthew C.; Khavinson, Dmitry S.; Seco, Daniel; Sola, Alan
 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 theoryCategories:46E22, 30J05

2. CMB 2008 (vol 51 pp. 481)

Bayart, Frédéric
 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 $H^\infty(\bn)$. Keywords:inner functions, automorphisms of the ball, universalityCategories:32A35, 30D50, 47B38

3. CMB 2005 (vol 48 pp. 409)

Gauthier, P. M.; Xiao, J.
 The Existence of Universal Inner Functions on the Unit Ball of $\mathbb{C}^n$ It is shown that there exists an inner function $I$ defined on the unit ball ${\bf B}^n$ of ${\mathbb C}^n$ such that each function holomorphic on ${\bf B}^n$ and bounded by $1$ can be approximated by non-Euclidean translates" of $I$. Keywords:universal inner functionsCategories:32A35, 30D50, 47B38
 top of page | contact us | privacy | site map |