Search: MSC category 30F35
( Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx] )
1. CJM 2003 (vol 55 pp. 576)
 Lukashov, A. L.; Peherstorfer, F.

Automorphic Orthogonal and Extremal Polynomials
It is well known that many polynomials which solve extremal problems
on a single interval as the Chebyshev or the BernsteinSzeg\"o
polynomials can be represented by trigonometric functions and their
inverses. On two intervals one has elliptic instead of trigonometric
functions. In this paper we show that the counterparts of the Chebyshev
and BernsteinSzeg\"o polynomials for several intervals can be represented
with the help of automorphic functions, socalled SchottkyBurnside
functions. Based on this representation and using the SchottkyBurnside
automorphic functions as a tool several extremal properties of such
polynomials as orthogonality properties, extremal properties with
respect to the maximum norm, behaviour of zeros and recurrence
coefficients {\it etc.} are derived.
Categories:42C05, 30F35, 31A15, 41A21, 41A50 

2. CJM 1998 (vol 50 pp. 449)
3. CJM 1997 (vol 49 pp. 55)
 Chen, Huaihui; Gauthier, Paul M.

Normal Functions: $L^p$ Estimates
For a meromorphic (or harmonic) function $f$, let us call the dilation
of $f$ at $z$ the ratio of the (spherical) metric at $f(z)$ and the
(hyperbolic) metric at $z$. Inequalities are known which estimate
the $\sup$ norm of the dilation in terms of its $L^p$ norm, for $p>2$,
while capitalizing on the symmetries of $f$. In the present paper
we weaken the hypothesis by showing that such estimates persist
even if the $L^p$ norms are taken only over the set of $z$ on which
$f$ takes values in a fixed spherical disk. Naturally, the bigger
the disk, the better the estimate. Also, We give estimates for
holomorphic functions without zeros and for harmonic functions in
the case that $p=2$.
Categories:30D45, 30F35 
