Godefroy, G.
Some applications of Simons' inequality
(pp. 59-78)
A B S T R A C T S
THE INTERVAL [0,1] ADMITS NO FUNCTORIAL EMBEDDING INTO
A FINITE-DIMENSIONAL OR METRIZABLE TOPOLOGICAL GROUP
Taras Banakh
tbanakh@franko.lviv.ua ,
Michael Zarichnyi
topos@franko.lviv.ua
2000 Mathematics Subject Classification: 18B30,
22A05, 54C20, 54E35, 54F45, 54H11.
Key words:
topological group, functorial embedding.
An embedding X Ì G of a topological space X into a
topological group G is called functorial if every
homeomorphism of X extends to a continuous group
homomorphism of G. It is shown that the interval [0,1] admits
no functorial embedding into a finite-dimensional or
metrizable topological group.
NEW BOUNDS FOR THE MAXIMUM SIZE OF TERNARY CONSTANT WEIGHT CODES
Galina Bogdanova
lpmivt@vt.bia-bg.com
2000 Mathematics Subject Classification: 94B65.
Key words:
Ternary codes, lexicographic codes, constant-weight codes.
Optimal ternary constant-weight lexicogarphic codes have been constructed.
New bounds for the maximum size of ternary constant-weight codes are
obtained.
Tables of bounds on A_{3}(n,d,w) are given for d = 3,4,6.
THE JNR PROPERTY AND THE BOREL STRUCTURE OF A BANACH SPACE
L. Oncina
luis@fcu.um.es
2000 Mathematics Subject Classification: 46B20.
Key words:
Borel sets, countable cover by
sets of small local diameter, topological invariants of the
weak topology.
In this paper we study the property of having a countable cover by sets of
small local diameter (SLD for short). We show that in the context of Banach
spaces (JNR property) it implies that the Banach space is
ech-analytic. We also prove that to have the JNR property, to be
s-fragmentable and to
have the same Borel sets for the weak and the norm topologies, they all are
topological invariants of the weak topology. Finally, by means of ``good''
injections into c_{0}(G), we give a great
class of Banach spaces
with the JNR property.
ON FINITE ELEMENT METHODS FOR 2ND ORDER (SEMI--)PERIODIC EIGENVALUE PROBLEMS
H. De Schepper
hds@cage.rug.ac.be
2000 Mathematics Subject Classification:
65N25, 65N30.
Key words:
Finite element methods, eigenvalue
problems, periodic boundary conditions.
We deal with a class of elliptic eigenvalue problems (EVPs) on a
rectangle W Ì R^{2},
with periodic or semi-periodic boundary conditions (BCs) on
¶W.
First, for both types of EVPs, we pass to a proper variational
formulation which is shown to fit into the general framework of
abstract EVPs for symmetric, bounded, strongly coercive bilinear
forms in Hilbert spaces, see, e.g., [13,§ 6.2]. Next,
we consider finite element methods (FEMs) without and with numerical
quadrature. The aim of the paper is to show that well-known error
estimates, established for the finite element approximation of elliptic
EVPs with classical BCs, hold for the present types of EVPs too.
Some attention is also paid to the computational aspects of the resulting
algebraic EVP. Finally, the analysis is illustrated by two non-trivial
numerical examples, the exact eigenpairs of which can be determined.
ON THE EXPONENTIAL BOUND OF THE CUTOFF RESOLVANT
Georgi Vodev
vodev@math.univ-nantes.fr
2000 Mathematics Subject Classification:
35P25, 35J15, 47F05.
Key words:
cutoff resolvent, resonances.
A simpler proof of a result of Burq
[1] is presented.
SOME APPLICATIONS OF SIMONS' INEQUALITY
Gilles Godefroy
gig@ccr.jussieu.fr
2000 Mathematics Subject Classification:
46B20.
Key words:
Boundaries, smooth norms, norm-attaining linear forms.
We survey several applications of Simons' inequality and state
related open problems. We show that if a Banach space X has a strongly
sub-differentiable norm, then every bounded weakly closed subset of X is
an intersection of finite union of balls.
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