24 x 17 cm. Approx. 290 pages. Paperback.
ISBN 978-3-11-019124-0 (ISBN10: 3-11-019124-5)
Series: de Gruyter Textbook
Language: English
to be published February 2007
This textbook presents a first introduction to PDEs on an
elementary level, enabling the reader to understand what partial
differential equations are, where they come from and how they can
be solved. The intention is that the reader understands the basic
principles which are valid for particular types of PDEs, and to
acquire some classical methods to solve them, thus the authors
restrict their considerations to fundamental types of equations
and basic methods. Only basic facts from calculus and linear
ordinary differential equations of first and second order are
needed as a prerequisite.
The book is addressed to students who intend to specialize in
mathematics as well as to students of physics, engineering, and
economics.
Proceedings of the 'Integers Conference 2005' in Celebration
of the 70th Birthday of Ronald Graham, Carrollton, Georgia,
October 27-30, 2005
24 x 17 cm. Approx. 400 pages. Cloth. Euro [D] 168.00 / sFr 269.00
/ for USA, Canada, Mexico US$ 186.00. *
ISBN 978-3-11-019029-8 (ISBN10: 3-11-019029-X)
Series: [de Gruyter Proceedings in Mathematics]
Subjects: Mathematics / Algebra, Number theory
Mathematics / Combinatorics and Graph Theory
Language: English
to be published February 2007
This carefully edited volume contains selected refereed papers
based on lectures presented by many distinguished speakers at the
"Integers Conference 2005", an international conference
in combinatorial number theory. The conference was held in
celebration of the 70th birthday of Ronald Graham, a leader in
several fields of mathematics.
Asterisque 305 (2006), vi+138 pages
Acheter l'ouvrage
Resume :
Calcul fonctionnel et fonctions carrees dans les espaces Lp non
commutatifs
Nous etudions les operateurs sectoriels et les semigroupes
operant sur un espace Lp non commutatif. Nous introduisons de
nouvelles fonctions carrees adaptees a ce contexte et etudions
leurs interactions avec le calcul fonctionnel . Nous obtenons des
extensions de travaux fameux de Cowling, Doust, McIntoch et Yagi
qui concernaient le cas commutatif. Cette etude necessite
l'introduction de variantes de la Rademacher sectorialite et
l'usage des structures matricielles sur les espaces Lp non
commutatifs. Nous traitons de facon approfondie les semigroupes
de diffusion non commutatifs. Il s'agit des semigroupes
d'operateurs normaux et auto-adjoints operant sur une algebre de
von Neumann semifinie , tels que est une contraction pour tout et
pour tout . Nous presentons et etudions plusieurs exemples de
tels semigroupes, pour lesquels nous sommes en mesure d'etablir
une propriete de calcul borne, ainsi que des estimations
quadratiques. Cette etude inclut certains semigroupes engendres
par des operateurs Hamiltoniens ou des multiplicateurs de Schur,
des semigroupes d'Ornstein-Uhlenbeck operant sur les algebres de
von Neumann de q-deformation de Bozejko-Speicher, et le
semigroupe de Poisson non commutatif defini sur l'algebre de von
Neumann d'un groupe libre.
Mots clefs : calcul fonctionnel , espaces Lp non commutatifs,
fonctions carrees, operateurs sectoriels, semigroupes de
diffusion, fonctions completement bornees, multiplicateurs
Abstract:
We investigate sectorial operators and semigroups acting on
noncommutative Lp-spaces. We introduce new square functions in
this context and study their connection with functional calculus,
extending some famous work by Cowling, Doust, McIntoch and Yagi
concerning commutative Lp-spaces. This requires natural variants
of Rademacher sectoriality and the use of the matricial structure
of noncommutative Lp-spaces. We mainly focus on noncommutative
diffusion semigroups, that is, semigroups of normal selfadjoint
operators on a semifinite von Neumann algebra such that is a
contraction for any and any . We discuss several examples of such
semigroups for which we establish bounded functional calculus and
square function estimates. This includes semigroups generated by
certain Hamiltonians or Schur multipliers, q-Ornstein-Uhlenbeck
semigroups acting on the q-deformed von Neumann algebras of
Bozejko-Speicher, and the noncommutative Poisson semigroup acting
on the group von Neumann algebra of a free group.
Key words: functional calculus, noncommutative Lp-spaces, square
functions, sectorial operators, diffusion semigroups, completely
bounded maps, multipliers
ISBN : 978-2-85629-189-4
Memoires de la SMF 105 (2006), vi+89 pages
Resume :
Etude quantitative de la metastabilite des processus reversibles
au moyen du complexe de Witten : le cas a bord.
Cet article prolonge des travaux anterieurs de Bovier-Eckhoff-Gayrard-Klein,
Bovier-Gayrard-Klein et Helffer-Klein-Nier. L'objet principal en
est l'analyse des petites valeurs propres du Laplacien associe a
la forme quadratique
ou est un domaine borne regulier et f est une fonction de Morse
sur . Les travaux precedents traitaient le cas d'une variete
compacte M sans bord ou le cas . Ici nous analysons le cas d'une
variete compacte a bord. Apres l'introduction d'un complexe de
cohomologie de Witten adapte au cas a bord, nous donnons une
description tres precise des valeurs propres exponentiellement
petites. En particulier, nous traitons l'effet du bord sur les
developpements asymptotiques.
Mots clefs : Complexe de Witten, Developpements semiclassiques,
valeurs propres exponentiellement petites, varietes a bord
Abstract:
This article is a continuation of previous works by Bovier-Eckhoff-Gayrard-Klein,
Bovier-Gayrard-Klein and Helffer-Klein-Nier. The main object is
the analysis of the small eigenvalues (as ) of the Laplacian
attached to the quadratic form
where is a bounded connected open set with -boundary and f is a
Morse function on . The previous works were devoted to the case
of a manifold M which is compact but without boundary or . Our
aim is here to analyze the case with boundary. After the
introduction of a Witten cohomology complex adapted to the case
with boundary, we give a very accurate asymptotics for the
exponentially small eigenvalues. In particular, we analyze the
effect of the boundary in the asymptotics.
Key words: Witten complex, Semiclassical expansion, exponentially
small quantities, manifolds with boundary
ISBN : 978-2-85629-218-1