Asterisque 344 (2012), viii+241 pages
ISBN : 978-2-85629-343-0
Abstract:
The goal of this work is to treat the main boundary value problems for the Stokes system, i.e.,
the Dirichlet problem with -data and nontangential maximal function estimates,
the Neumann problem with -data and nontangential maximal function estimates,
the Regularity problem with -data and nontangential maximal function estimates,
the transmission problem with -data and nontangential maximal function estimates,
the Poisson problem with Dirichlet condition in Besov-Triebel-Lizorkin spaces,
the Poisson problem with Neumann condition in Besov-Triebel-Lizorkin spaces,
in Lipschitz domains of arbitrary topology in , for each . Our approach relies on boundary integral methods and yields constructive solutions to the aforementioned problems.
Stokes system, Lipschitz domains, boundary problems, layer potentials, Besov-Triebel-Lizorkin spaces
Panoramas et syntheses 33 (2011)
ISBN : 978-2-85629-346-1
The book exposes recent results about hyperbolic polynomials in one real variable, i.e. having all their roots real. It contains a study of the stratification and the geometric properties of the domain in of the values of the coefficients for which the polynomial is hyperbolic. Similar studies are performed w.r.t. very hyperbolic polynomials, i.e. hyperbolic and having hyperbolic primitives of any order, and w.r.t. stably hyperbolic ones, i.e. real polynomials of degree which become hyperbolic after multiplication by and addition of a suitable polynomial of degree . New results are presented concerning the Schur-Szeg? composition of polynomials, in particular of hyperbolic ones, and of certain entire functions. The question what can be the arrangement of the roots of the polynomials , , , is studied for with the help of the discriminant sets .
hyperbolic polynomial in one variable, very hyperbolic polynomial, stably hyperbolic polynomial, stratification, Whitney property, Schur-Szeg? composition, (finite) multiplier sequence, Laguerre-Polya class, discriminant set, root arrangement
Asterisque 345 (2012), xi+147 pages
ISBN : 978-2-85629-345-4
On a complex manifold , a -algebroid is an algebroid stack locally equivalent to the sheaf endowed with a star-product and a -module is an object of the derived category . The main results are:
the notion of cohomologically complete -modules which allows one to deduce various properties of such a module from the corresponding properties of the -module ,
a finiteness theorem, which asserts that the convolution of two coherent -kernels defined on manifolds (), satisfying a suitable properness assumption, is coherent (a non commutative Grauert's theorem),
the construction of the dualizing complex for coherent -modules and a duality theorem which asserts that duality commutes with convolution (a non commutative Serre's theorem),
the construction of the Hochschild class of coherent -modules and the theorem which asserts that Hochschild class commutes with convolution,
in the commutative case, the link between Hochschild classes and Chern and Euler classes,
in the symplectic case, the constructibility (and perversity) of the complex of solutions of an holonomic -module into another one after localizing with respect to .
Hence, these Notes could be considered both as an introduction to non commutative complex analytic geometry and to the study of microdifferential systems on complex Poisson manifolds.
Deformation quantization, DQ-modules, complex Poisson manifolds, algebroid stacks, convolution of kernels, dualizing complexes, Hochschild homology, Euler classes, holonomic modules
Published: July 2012
336 pages
9781571462497
paperback
The editors dedicate this volume to the late S.?S. Chern, one of the great mathematicians of the twentieth century, and a leader in the field of differential geometry. Chern made seminal advances in areas such as web geometry, integral geometry, complex geometry, Riemannian geometry, and Finsler geometry. He is well-known for the Chern-Simons theory, the Chern-Weil theory, and Chern classes. His brilliant research and teaching have exerted a deep and lasting influence on mathematics.
Presented herein are survey papers by mathematicians from around the world, particularly from China, who review the present state of the areas in which Chern worked, and discuss the various directions which those fields will take in the future. This collection contains valuable information useful to graduate students and researchers.
Series: SpringerBriefs in Statistics
2012, 2012, XII, 106 p.
Available Formats:
Softcover
Self-contained discussion
Includes numerous examples and applications.
This monograph provides an extensive treatment of the theory and applications of the celebrated Borel-Cantelli Lemma. Starting from some of the basic facts of the axiomatic probability theory, it embodies the classical versions of these lemma, together with the well known as well as the most recent extensions of them due to Barndorff-Nielsen, Balakrishnan and Stepanov, Erdos and Renyi, Kochen and Stone, Petrov and the present author. The versions of the second Borel-Cantelli Lemma for pair wise negative quadrant dependent sequences, weakly *-mixing sequences, mixing sequences (due to Renyi) and for many other dependent sequences are all included. The special feature of the book is a detailed discussion of a strengthened form of the second Borel-Cantelli Lemma and the conditional form of the Borel-Cantelli Lemmas due to Levy, Chen and Serfling. All these results are well illustrated by means of many interesting examples. All the proofs are rigorous, complete and lucid. An extensive list of research papers, some of which are forthcoming, is provided. The book can be used for a self study and as an invaluable research reference on the present topic.