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1. CJM Online first
A Finite-time Condition for Exponential Trichotomy in Infinite Dynamical Systems In this article we study exponential trichotomy for infinite dimensional
discrete time dynamical systems. The goal of this article is to prove that
finite time exponential trichotomy conditions allow to derive exponential
trichotomy for any times. We present an application to the case of pseudo
orbits in some neighborhood of a normally hyperbolic set.
Keywords:exponential trichotomy, exponential dichotomy, discrete time dynamical systems, difference equations Categories:34D09, 34A10 |
2. CJM 2012 (vol 65 pp. 82)
The Ranks of the Homotopy Groups of a Finite Dimensional Complex Let $X$ be an
$n$-dimensional, finite, simply connected CW complex and set
$\alpha_X =\limsup_i \frac{\log\mbox{ rank}\, \pi_i(X)}{i}$. When
$0\lt \alpha_X\lt \infty$, we give upper and lower bound for $
\sum_{i=k+2}^{k+n} \textrm{rank}\, \pi_i(X) $ for $k$ sufficiently
large. We show also for any $r$ that $\alpha_X$ can be estimated
from the integers rk$\,\pi_i(X)$, $i\leq nr$ with an error bound
depending explicitly on $r$.
Keywords:homotopy groups, graded Lie algebra, exponential growth, LS category Categories:55P35, 55P62, , , , 17B70 |
3. CJM 2010 (vol 63 pp. 38)
Asymptotic Formulae for Pairs of Diagonal Cubic Equations
We investigate the number of integral solutions possessed by a
pair of diagonal cubic equations in a large box. Provided that the number of
variables in the system is at least fourteen, and in addition the number of
variables in any non-trivial linear combination of the underlying forms is at
least eight, we obtain an asymptotic formula for the number of integral
solutions consistent with the product of local densities associated with the
system.
Keywords:exponential sums, Diophantine equations Categories:11D72, 11P55 |
4. CJM 2010 (vol 62 pp. 261)
Erratum to: On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials |
Erratum to: On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials No abstract.
Keywords:Complex Oscillation theory, Exponent of convergence of zeros, zero distribution of Bessel and Confluent hypergeometric functions, Lommel transform, Bessel polynomials, Heine Problem Categories:34M10, 33C15, 33C47 |
5. CJM 2009 (vol 62 pp. 19)
Solutions for Semilinear Elliptic Systems with Critical Sobolev Exponent and Hardy Potential In this paper we consider an elliptic system with an inverse square potential and
critical Sobolev exponent in a bounded domain of $\mathbb{R}^N$. By variational
methods we study the existence results.
Keywords:critical Sobolev exponent, Palais--Smale condition, Linking theorem, Hardy potential Categories:35B25, 35B33, 35J50, 35J60 |
6. CJM 2009 (vol 61 pp. 336)
The Large Sieve Inequality for the Exponential Sequence $\lambda^{[O(n^{15/14+o(1)})]}$ Modulo Primes |
The Large Sieve Inequality for the Exponential Sequence $\lambda^{[O(n^{15/14+o(1)})]}$ Modulo Primes Let $\lambda$ be a fixed integer exceeding $1$ and $s_n$ any
strictly increasing sequence of positive integers satisfying $s_n\le
n^{15/14+o(1)}.$ In this paper we give a version of the large sieve
inequality for the sequence $\lambda^{s_n}.$ In particular, we
obtain nontrivial estimates of the associated trigonometric sums
``on average" and establish equidistribution properties of the
numbers $\lambda^{s_n} , n\le p(\log p)^{2+\varepsilon}$,
modulo $p$ for most primes $p.$
Keywords:Large sieve, exponential sums Categories:11L07, 11N36 |
7. CJM 2006 (vol 58 pp. 726)
On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials |
On Value Distribution Theory of Second Order Periodic ODEs, Special Functions and Orthogonal Polynomials We show that the value distribution (complex oscillation) of
solutions of certain periodic second order ordinary differential
equations studied by Bank, Laine and Langley is closely
related to confluent hypergeometric functions, Bessel functions
and Bessel polynomials. As a result, we give a complete
characterization of the zero-distribution in the sense of
Nevanlinna theory of the solutions for two classes of the ODEs.
Our approach uses special functions and their asymptotics. New
results concerning finiteness of the number of zeros
(finite-zeros) problem of Bessel and Coulomb wave functions with
respect to the parameters are also obtained as a consequence. We
demonstrate that the problem for the remaining class of ODEs not
covered by the above ``special function approach" can be
described by a classical Heine problem for differential
equations that admit polynomial solutions.
Keywords:Complex Oscillation theory, Exponent of convergence of zeros, zero distribution of Bessel and Confluent hypergeometric functions, Lommel transform, Bessel polynomials, Heine Proble Categories:34M10, 33C15, 33C47 |
8. CJM 2001 (vol 53 pp. 944)
ReprÃ©sentations irrÃ©ductibles bornÃ©es des groupes de Lie exponentiels Let $G$ be a solvable exponential Lie group. We characterize all the
continuous topologically irreducible bounded representations $(T,
\calU)$ of $G$ on a Banach space $\calU$ by giving a $G$-orbit in
$\frn^*$ ($\frn$ being the nilradical of $\frg$), a topologically
irreducible representation of $L^1(\RR^n, \o)$, for a certain weight
$\o$ and a certain $n \in \NN$, and a topologically simple extension
norm. If $G$ is not symmetric, \ie, if the weight $\o$ is
exponential, we get a new type of representations which are
fundamentally different from the induced representations.
Soit $G$ un groupe de Lie r\'esoluble exponentiel. Nous
caract\'erisons toutes les repr\'esentations $(T, \calU)$ continues
born\'ees topologiquement irr\'eductibles de $G$ dans un espace de
Banach $\calU$ \`a l'aide d'une $G$-orbite dans $\frn^*$ ($\frn$
\'etant le radical nilpotent de $\frg$), d'une repr\'esentation
topologiquement irr\'eductible de $L^1(\RR^n, \o)$, pour un certain
poids $\o$ et un certain $n \in \NN$, d'une norme d'extension
topologiquement simple. Si $G$ n'est pas sym\'etrique, c. \`a d. si
le poids $\o$ est exponentiel, nous obtenons un nouveau type de
repr\'esentations qui sont fondamentalement diff\'erentes des
repr\'esentations induites.
Keywords:groupe de Lie rÃ©soluble exponentiel, reprÃ©sentation bornÃ©e topologiquement irrÃ©ductible, orbite, norme d'extension, sous-espace invariant, idÃ©al premier, idÃ©al primitif Category:43A20 |