scispace - formally typeset
Search or ask a question
Institution

Institut Élie Cartan de Lorraine

FacilityVandœuvre-lès-Nancy, France
About: Institut Élie Cartan de Lorraine is a facility organization based out in Vandœuvre-lès-Nancy, France. It is known for research contribution in the topics: Boundary value problem & Brownian motion. The organization has 345 authors who have published 1084 publications receiving 15512 citations. The organization is also known as: Institut Élie-Cartan de Nancy.


Papers
More filters
Book
14 Jul 2009
TL;DR: The main topics of interest about observation and control operators are admissibility, observability, controllability, stabilizability and detectability as discussed by the authors, which is a mature area of functional analysis, which is still very active.
Abstract: The evolution of the state of many systems modeled by linear partial difierentialequations (PDEs) or linear delay-difierential equations can be described by operatorsemigroups. The state of such a system is an element in an inflnite-dimensionalnormed space, whence the name \inflnite-dimensional linear system".The study of operator semigroups is a mature area of functional analysis, which isstill very active. The study of observation and control operators for such semigroupsis relatively more recent. These operators are needed to model the interactionof a system with the surrounding world via outputs or inputs. The main topicsof interest about observation and control operators are admissibility, observability,controllability, stabilizability and detectability. Observation and control operatorsare an essential ingredient of well-posed linear systems (or more generally systemnodes). Inthisbookwedealonlywithadmissibility, observabilityandcontrollability.We deal only with operator semigroups acting on Hilbert spaces.This book is meant to be an elementary introduction into the topics mentionedabove. By \elementary" we mean that we assume no prior knowledge of flnite-dimensional control theory, and no prior knowledge of operator semigroups or ofunbounded operators. We introduce everything needed from these areas. We doassume that the reader has a basic understanding of bounded operators on Hilbertspaces, difierential equations, Fourier and Laplace transforms, distributions andSobolev spaces on

1,174 citations

Book
18 Jul 2006
TL;DR: The first eigenvalue of the Laplacian-Dirichlet operator was defined in this paper and the other Dirichlet eigenvalues were defined in this paper.
Abstract: Eigenvalues of elliptic operators.- Tools.- The first eigenvalue of the Laplacian-Dirichlet.- The second eigenvalue of the Laplacian-Dirichlet.- The other Dirichlet eigenvalues.- Functions of Dirichlet eigenvalues.- Other boundary conditions for the Laplacian.- Eigenvalues of Schrodinger operators.- Non-homogeneous strings and membranes.- Optimal conductivity.- The bi-Laplacian operator.

849 citations

Book
01 May 2012
TL;DR: In this article, the authors provide an ideal introduction both to Stein's method and Malliavin calculus, from the standpoint of normal approximations on a Gaussian space, and explain the connections between Stein's methods and Mallian calculus of variations.
Abstract: Stein's method is a collection of probabilistic techniques that allow one to assess the distance between two probability distributions by means of differential operators. In 2007, the authors discovered that one can combine Stein's method with the powerful Malliavin calculus of variations, in order to deduce quantitative central limit theorems involving functionals of general Gaussian fields. This book provides an ideal introduction both to Stein's method and Malliavin calculus, from the standpoint of normal approximations on a Gaussian space. Many recent developments and applications are studied in detail, for instance: fourth moment theorems on the Wiener chaos, density estimates, Breuer–Major theorems for fractional processes, recursive cumulant computations, optimal rates and universality results for homogeneous sums. Largely self-contained, the book is perfect for self-study. It will appeal to researchers and graduate students in probability and statistics, especially those who wish to understand the connections between Stein's method and Malliavin calculus.

712 citations

BookDOI
01 Jan 2005

595 citations


Authors

Showing all 361 results

NameH-indexPapersCitations
Ivan Nourdin442176139
Marius Tucsnak331143907
Victor Nistor311583352
Xavier Antoine301252992
Jan Sokołowski302036056
Nicolas Fournier291063044
Gérald Tenenbaum291735100
Lionel Rosier291263956
Vicente Cortés271182356
Gauthier Sallet27702007
Antoine Henrot261283268
Samy Tindel261682656
Bruno Scherrer25691447
Mario Sigalotti251802082
Takéo Takahashi24871673
Network Information
Related Institutions (5)
Courant Institute of Mathematical Sciences
7.7K papers, 439.7K citations

88% related

École normale supérieure de Cachan
5.5K papers, 175.9K citations

85% related

École Polytechnique
39.2K papers, 1.2M citations

83% related

Institute for Advanced Study
7.2K papers, 621.1K citations

80% related

Performance
Metrics
No. of papers from the Institution in previous years
YearPapers
20234
202232
202152
202067
201976
201884