Expand all Collapse all | Results 51 - 60 of 60 |
51. CMB 2001 (vol 44 pp. 126)
Each Copy of the Real Line in $\C^2$ is Removable Around 1995, Professors Lupacciolu, Chirka and Stout showed that a
closed subset of $\C^N$ ($N\geq 2$) is removable for holomorphic
functions, if its topological dimension is less than or equal to
$N-2$. Besides, they asked whether closed subsets of $\C^2$
homeomorphic to the real line (the simplest 1-dimensional sets) are
removable for holomorphic functions. In this paper we propose a
positive answer to that question.
Keywords:holomorphic function, removable set Category:32D20 |
52. CMB 2000 (vol 43 pp. 294)
Fixed Points of Commuting Holomorphic Maps Without Boundary Regularity We identify a class of domains of $\C^n$ in which any two commuting
holomorphic self-maps have a common fixed point.
Keywords:Holomorphic self-maps, commuting functions, fixed points, Wolff point, Julia's Lemma Categories:32A10, 32A40, 32H15, 32A30 |
53. CMB 2000 (vol 43 pp. 174)
Stable Parabolic Bundles over Elliptic Surfaces and over Riemann Surfaces We show that the use of orbifold bundles enables some questions to
be reduced to the case of flat bundles. The identification of
moduli spaces of certain parabolic bundles over elliptic surfaces
is achieved using this method.
Categories:14J27, 32L07, 14H60, 14D20 |
54. CMB 2000 (vol 43 pp. 47)
A Property of Lie Group Orbits Let $G$ be a real Lie group and $X$ a real analytic manifold.
Suppose that $G$ acts analytically on $X$ with finitely many
orbits. Then the orbits are subanalytic in $X$. As a consequence
we show that the micro-support of a $G$-equivariant sheaf on $X$ is
contained in the conormal variety of the $G$-action.
Categories:32B20, 22E15 |
55. CMB 1999 (vol 42 pp. 499)
Characterizations of Simple Isolated Line Singularities A line singularity is a function germ $f\colon(\CC ^{n+1},0) \lra\CC$
with a smooth $1$-dimensional critical set $\Sigma=\{(x,y)\in \CC\times
\CC^n \mid y=0\}$. An isolated line singularity is defined by the
condition that for every $x \neq 0$, the germ of $f$ at $(x,0)$ is
equivalent to $y_1^2 +\cdots+y_n ^2$. Simple isolated line
singularities were classified by Dirk Siersma and are analogous
of the famous $A-D-E$ singularities. We give two new
characterizations of simple isolated line singularities.
Categories:32S25, 14B05 |
56. CMB 1999 (vol 42 pp. 97)
On Analytic Functions of Bergman $\BMO$ in the Ball Let $B = B_n$ be the open unit ball of $\bbd C^n$ with
volume measure $\nu$, $U = B_1$ and ${\cal B}$ be the Bloch space on
$U$. ${\cal A}^{2, \alpha} (B)$, $1 \leq \alpha < \infty$, is defined
as the set of holomorphic $f\colon B \rightarrow \bbd C$ for which
$$
\int_B \vert f(z) \vert^2 \left( \frac 1{\vert z\vert}
\log \frac 1{1 - \vert z\vert } \right)^{-\alpha}
\frac {d\nu (z)}{1-\vert z\vert} < \infty
$$
if $0 < \alpha <\infty$ and ${\cal A}^{2, 1} (B) = H^2(B)$, the Hardy
space. Our objective of this note is to characterize, in terms of
the Bergman distance, those holomorphic $f\colon B \rightarrow U$ for
which the composition operator $C_f \colon {\cal B} \rightarrow
{\cal A}^{2, \alpha}(B)$ defined by $C_f (g) = g\circ f$,
$g \in {\cal B}$, is bounded. Our result has a corollary that
characterize the set of analytic functions of bounded mean
oscillation with respect to the Bergman metric.
Keywords:Bergman distance, \BMOA$, Hardy space, Bloch function Category:32A37 |
57. CMB 1998 (vol 41 pp. 129)
Pluriharmonic symbols of commuting Toeplitz type operators on the weighted Bergman spaces A class of Toeplitz type operators acting on the
weighted Bergman spaces of the unit ball in the $n$-dimensional complex
space is considered and two pluriharmonic symbols of commuting
Toeplitz type operators are completely characterized.
Keywords:Pluriharmonic functions, Weighted Bergman spaces, Toeplitz type operators. Categories:47B38, 32A37 |
58. 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 |
59. CMB 1997 (vol 40 pp. 129)
Sur les caractÃ¨res d'une algÃ¨bre de Banach A new proof for the Gleason-Kahane-\.Zelazko theorem concerning the
characters of a Banach algebra is given. A theorem due to P\'olya and
Saxer is used instead of the Hadamard factorization theorem.
Categories:46H05, 32A15 |
60. CMB 1997 (vol 40 pp. 117)
Un lemme de Schwarz pour les boules-unitÃ©s ouvertes Let $B_1$ and $B_2$ be the open unit balls of ${\bbd C}^{n_1}$ and
${\bbd C}^{n_2}$ for the norms $\Vert\,{.}\,\Vert_1$ and $\Vert\,{.}\,
\Vert_2$. Let $f \colon B_1 \rightarrow B_2$ be a holomorphic
mapping such that $f(0)=0$. It is well known that, for every $z \in B_1$,
$\Vert f(z)\Vert_2 \leq \Vert z \Vert_1$, and $\Vert f'(0)\Vert \leq
1$.
In this paper, I prove the converse of this result. Let $f \colon B_1
\rightarrow B_2$ be a holomorphic mapping such that $f'(0)$ is an
isometry. If $B_2$ is strictly convex, I prove that $f(0) =0$ and
that $f$ is linear. I also define the rank of a point $x$ belonging to the
boundary of $B_1$ or $B_2$. Under some hypotheses on the ranks, I
prove that a holomorphic mapping such that $f(0) = 0$ and that $f'(0)$ is
an isometry is linear.
Categories:32H15, 32H02 |