This book concerns discrete-time homogeneous Markov chains that admit an invariant probability measure. The main objective is to give a systematic, self-contained presentation on some key issues about the ergodic behavior of that class of Markov chains. These issues include, in particular, the various types of convergence of expected and pathwise occupation measures, and ergodic decompositions of the state space.
This book concerns discrete-time homogeneous Markov chains that admit an invariant probability measure. The main objective is to give a systematic,...
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2004.
This book studies regularity properties of Mumford-Shah minimizers. The Mumford-Shah functional was introduced in the 1980s as a tool for automatic image segmentation, but its study gave rise to many interesting questions of analysis and geometric measure theory. The main object under scrutiny is a free boundary K where the minimizer may have jumps. The book presents an extensive description of the known regularity properties of the singular sets K, and the techniques to get them. Some time is spent on the C...
Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2004.
This book studies regularity properties of Mumford-Shah minimizers. The ...
This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems" held in July 2003 at the University of Algarve, Faro, Portugal, as a satellite workshop of the XIV International Congress on Mathematical Physics. In it, recent developments in the theory of infinite dimensional algebras, and their applications to quantum integrable systems, are reviewed by leading experts in the field.
This volume presents the invited lectures of the workshop "Infinite Dimensional Algebras and Quantum Integrable Systems" held in July 2003 at the U...
Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R and a great deal of work has been devoted to their study. From the mathematical point of view, the main interest relies on the fact that the tools of Nonlinear Functional Analysis, based on compactness arguments, in general cannot be used, at least in a straightforward way, and some new techniques have to be developed. n On the other hand, there are several elliptic problems on R which are p- turbative in nature. In some cases there is a...
Several important problems arising in Physics, Di?erential Geometry and other n topics lead to consider semilinear variational elliptic equations on R...
This book has been awarded the Ferran Sunyer i Balaguer 2005 prize.
The aim of this book is to give an overview of selected topics on the topology of real and complex isolated singularities, with emphasis on its relations to other branches of geometry and topology. The first chapters are mostly devoted to complex singularities and a myriad of results spread in a vast literature, which are presented here in a unified way, accessible to non-specialists. Among the topics are the fibration theorems of Milnor; the relation with 3-dimensional Lie groups; exotic spheres; spin structures...
This book has been awarded the Ferran Sunyer i Balaguer 2005 prize.
The aim of this book is to give an overview of selected topics on the topolo...
Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous fundamental contributions. The impact of his work is also visible in several articles in this book. Quantum fields are considered as genuine mathematical objects, whose various properties and relevant physical interpretations have to be studied in a well-defined mathematical framework.
Key topics: Analytic structures of QFT, renormalization group methods, gauge QFT, stability properties and extension of the axiomatic framework, QFT on models of curved spacetimes, QFT on...
Jacques Bros has greatly advanced our present understanding of rigorous quantum field theory through numerous fundamental contributions. The impact...
This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics.
This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in gr...
The algebra of primary cohomology operations computed by the well-known Steenrod algebra is one of the most powerful tools of algebraic topology. This book computes the algebra of secondary cohomology operations which enriches the structure of the Steenrod algebra in a new and unexpected way.
The book solves a long-standing problem on the algebra of secondary cohomology operations by developing a new algebraic theory of such operations. The results have strong impact on the Adams spectral sequence and hence on the computation of homotopy groups of spheres.
The algebra of primary cohomology operations computed by the well-known Steenrod algebra is one of the most powerful tools of algebraic topology. T...
The n-dimensionalmetaplectic groupSp(n, R) is the twofoldcoverof the sympl- n n tic group Sp(n, R), which is the group of linear transformations ofX = R xR that preserve the bilinear (alternate) form x y ( ), ( )] =? x, ? + y, ? . (0. 1) ? ? 2 n There is a unitary representation of Sp(n, R)intheHilbertspace L (R ), called the metaplectic representation, the image of which is the groupof transformations generated by the following ones: the linear changes of variables, the operators of multiplication by exponentials with pure imaginary quadratic forms in the ex- nent, and the Fourier...
The n-dimensionalmetaplectic groupSp(n, R) is the twofoldcoverof the sympl- n n tic group Sp(n, R), which is the group of linear transformations ofX =...
This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. It opens perspectives on several active areas of research in complex, Kahler and symplectic geometry. A large number of applications are also included, such as an analytic proof of Kodaira's embedding theorem, a solution of the Grauert-Riemenschneider and Shiffman conjectures, compactification of complete Kahler manifolds of pinched negative curvature, Berezin-Toeplitz quantization, weak Lefschetz theorems, and asymptotics of the Ray-Singer analytic...
This book examines holomorphic Morse inequalities and the asymptotic expansion of the Bergman kernel on manifolds by using the heat kernel. It open...
