Expand all Collapse all | Results 26 - 44 of 44 |
26. CMB 2005 (vol 48 pp. 409)
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 functions Categories:32A35, 30D50, 47B38 |
27. CMB 2004 (vol 47 pp. 152)
On Uniqueness of Meromorphic Functions with Shared Values in Some Angular Domains In this paper we investigate the uniqueness of transcendental
meromorphic function dealing with the shared values in some angular
domains instead of the whole complex plane.
Keywords:Nevanlinna theory, meromorphic function, shared value Category:30D35 |
28. CMB 2004 (vol 47 pp. 17)
Universal Singular Inner Functions We show that there exists a singular inner function $S$ which is
universal for noneuclidean translates; that is one for which the set
$\{S(\frac{z+z_n}{1+\bar z_nz}):n\in\mathbb{N}\}$ is locally uniformly dense
in the set of all zero-free holomorphic functions in $\mathbb{D}$ bounded by
one.
Category:30D50 |
29. CMB 2003 (vol 46 pp. 559)
On Density Conditions for Interpolation in the Ball In this paper we study interpolating sequences for two related spaces of
holomorphic functions in the unit ball of $\C^n$, $n>1$. We first give density
conditions for a sequence to be interpolating for the class $A^{-\infty}$ of
holomorphic functions with polynomial growth. The sufficient condition is
formally identical to the characterizing condition in dimension $1$, whereas the
necessary one goes along the lines of the results given by Li and Taylor for
some spaces of entire functions. In the second part of the paper we show that a
density condition, which for $n=1$ coincides with the characterizing condition
given by Seip, is sufficient for interpolation in the (weighted) Bergman space.
Categories:32A36, 32A38, 30E05 |
30. CMB 2003 (vol 46 pp. 95)
Cercles de remplissage for the Riemann Zeta Function The celebrated theorem of Picard asserts that each non-constant entire
function assumes every value infinitely often, with at most one
exception. The Riemann zeta function has this Picard behaviour in a
sequence of discs lying in the critical band and whose diameters tend
to zero. According to the Riemann hypothesis, the value zero would be
this (unique) exceptional value.
Keywords:cercles de remplissage, Riemann zeta function Category:30 |
31. CMB 2002 (vol 45 pp. 265)
On the Smirnov Class Defined by the Maximal Function H.~O.~Kim has shown that contrary to the case of
$H^p$-space, the Smirnov class $M$ defined by the radial maximal
function is essentially smaller than the classical Smirnov class
of the disk. In the paper we show that these two classes have the
same corresponding locally convex structure, {\it i.e.} they have the
same dual spaces and the same Fr\'echet envelopes. We describe a
general form of a continuous linear functional on $M$ and
multiplier from $M$ into $H^p$, $0 < p \leq \infty$.
Keywords:Smirnov class, maximal radial function, multipliers, dual space, FrÃ©chet envelope Categories:46E10, 30A78, 30A76 |
32. CMB 2002 (vol 45 pp. 89)
On Gunning's Prime Form in Genus $2$ Using a classical generalization of Jacobi's derivative formula, we
give an explicit expression for Gunning's prime form in genus 2 in
terms of theta functions and their derivatives.
Categories:14K25, 30F10 |
33. CMB 2002 (vol 45 pp. 154)
On the Poisson Integral of Step Functions and Minimal Surfaces Applications of minimal surface methods are made to obtain information
about univalent harmonic mappings. In the case where the mapping arises
as the Poisson integral of a step function, lower bounds for the number
of zeros of the dilatation are obtained in terms of the geometry of the
image.
Keywords:harmonic mappings, dilatation, minimal surfaces Categories:30C62, 31A05, 31A20, 49Q05 |
34. CMB 2002 (vol 45 pp. 36)
Modular Equations and Discrete, Genus-Zero Subgroups of $\SL(2,\mathbb{R})$ Containing $\Gamma(N)$ Let $G$ be a discrete subgroup of $\SL(2,\R)$ which contains
$\Gamma(N)$ for some $N$. If the genus of $X(G)$ is zero, then there
is a unique normalised generator of the field of $G$-automorphic
functions which is known as a normalised Hauptmodul. This paper gives
a characterisation of normalised Hauptmoduls as formal $q$ series
using modular polynomials.
Categories:11F03, 11F22, 30F35 |
35. CMB 2001 (vol 44 pp. 420)
Approximation by Meromorphic Functions With Mittag-Leffler Type Constraints Functions defined on closed sets are simultaneously approximated and
interpolated by meromorphic functions with prescribed poles and zeros
outside the set of approximation.
Categories:30D30, 30E10, 30E15 |
36. CMB 2000 (vol 43 pp. 183)
A Gauge Theoretic Proof of the Abel-Jacobi Theorem We present a new, simple proof of the classical Abel-Jacobi theorem
using some elementary gauge theoretic arguments.
Keywords:Abel-Jacobi theorem, abelian gauge theory Categories:58D27, 30F99 |
37. CMB 2000 (vol 43 pp. 115)
Perfect Non-Extremal Riemann Surfaces An infinite family of perfect, non-extremal Riemann surfaces
is constructed, the first examples of this type of surfaces.
The examples are based on normal subgroups of the modular group
$\PSL(2,{\sf Z})$ of level $6$. They provide non-Euclidean
analogues to the existence of perfect, non-extremal positive
definite quadratic forms. The analogy uses the function {\it syst\/}
which associates to every Riemann surface $M$ the length of a systole,
which is a shortest closed geodesic of $M$.
Categories:11H99, 11F06, 30F45 |
38. CMB 2000 (vol 43 pp. 105)
Sets of Uniqueness for Univalent Functions We observe that any set of uniqueness for the Dirichlet space $\cD$
is a set of uniqueness for the class $S$ of normalized univalent
holomorphic functions.
Categories:30C55, 30C15 |
39. CMB 1999 (vol 42 pp. 139)
Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions |
Essential Norm and Weak Compactness of Composition Operators on Weighted Banach Spaces of Analytic Functions Every weakly compact composition operator between weighted Banach
spaces $H_v^{\infty}$ of analytic functions with weighted sup-norms is
compact. Lower and upper estimates of the essential norm of
continuous composition operators are obtained. The norms of the point
evaluation functionals on the Banach space $H_v^{\infty}$ are also
estimated, thus permitting to get new characterizations of compact
composition operators between these spaces.
Keywords:weighted Banach spaces of holomorphic functions, composition operator, compact operator, weakly compact operator Categories:47B38, 30D55, 46E15 |
40. CMB 1999 (vol 42 pp. 3)
How the Roots of a Polynomial Vary with Its Coefficients: A Local Quantitative Result A well-known result, due to Ostrowski, states that if $\Vert P-Q
\Vert_2< \varepsilon$, then the roots $(x_j)$ of $P$ and $(y_j)$ of
$Q$ satisfy $|x_j -y_j|\le C n \varepsilon^{1/n}$, where $n$ is the
degree of $P$ and $Q$. Though there are cases where this estimate
is sharp, it can still be made more precise in general, in two
ways: first by using Bombieri's norm instead of the classical $l_1$
or $l_2$ norms, and second by taking into account the multiplicity
of each root. For instance, if $x$ is a simple root of $P$, we show
that $|x-y|< C \varepsilon$ instead of $\varepsilon^{1/n}$. The
proof uses the properties of Bombieri's scalar product and Walsh
Contraction Principle.
Category:30C10 |
41. CMB 1998 (vol 41 pp. 473)
Separating singularities of holomorphic functions We present a short proof for a classical result on separating
singularities of holomorphic functions. The proof is based on the
open mapping theorem and the fusion lemma of Roth, which is a basic
tool in complex approximation theory. The same method yields
similar separation results for other classes of functions.
Categories:30E99, 30E10 |
42. CMB 1997 (vol 40 pp. 475)
Coefficient multipliers of Bergman spaces $A^p$, II We show that the multiplier space $(A^1,X)=\{g:M_\infty(r,g'')
=O(1-r)^{-1}\}$, where $X$ is $\BMOA$, $\VMOA$, $B$, $B_0$ or disk algebra $A$.
We give the multipliers from $A^1$ to $A^q(H^q)(1\le q\le \infty)$, we
also give the multipliers from $l^p(1\le p\le 2), C_0, \BMOA$, and
$H^p(2\le p<\infty)$ into $A^q(1\le q\le 2)$.
Keywords:Multiplier, Bergman space, Hardy space, Bloch space, $\BMOA$. Categories:30H05, 30B10 |
43. CMB 1997 (vol 40 pp. 271)
Non-real periodic points of entire functions It is shown that if $f$ is an entire transcendental function, $l$ a straight
line in the complex plane, and $n\geq 2$, then $f$ has infinitely many
repelling periodic points of period $n$ that do not lie on $l$.
Categories:30D05, 58F23 |
44. CMB 1997 (vol 40 pp. 356)
Principe du maximum et lemme de Schwarz, a valeurs vectorielles Nous {\'e}tablissons un
th{\'e}or{\`e}me pour les fonctions holomorphes {\`a} valeurs dans une
partie convexe ferm{\'e}e. Ce th{\'e}or{\`e}me pr{\'e}cise
la position des coefficients de Taylor de telles fonctions et peut
{\^e}tre consid{\'e}r{\'e} comme une g{\'e}n{\'e}ralisation des
in{\'e}galit{\'e}s de Cauchy. Nous montrons alors comment ce
th{\'e}or{\`e}me permet de retrouver des versions connues du principe
du maximum et d'obtenir de nouveaux r{\'e}sultats sur les
applications holomorphes {\`a} valeurs vectorielles.
Keywords:Principe du maximum, lemme de Schwarz, points extr{Ã©maux. Categories:30C80, 32A30, 46G20, 52A07 |