Bøger i Progress in Mathematics serien

This monograph lays down the foundations of the theory of complex Kleinian groups, a newly born area of mathematics whose origin traces back to the work of Riemann, Poincare, Picard and many others. Kleinian groups are, classically, discrete groups of conformal automorphisms of the Riemann sphere, and these can be regarded too as being groups of holomorphic automorphisms of the complex projective line CP1. When going into higher dimensions, there is a dichotomy: Should we look at conformal automorphisms of the n-sphere?, or should we look at holomorphic automorphisms of higher dimensional complex projective spaces? These two theories are different in higher dimensions. In the first case we are talking about groups of isometries of real hyperbolic spaces, an area of mathematics with a long-standing tradition. In the second case we are talking about an area of mathematics that still is in its childhood, and this is the focus of study in this monograph. This brings together several important areas of mathematics, as for instance classical Kleinian group actions, complex hyperbolic geometry, chrystallographic groups and the uniformization problem for complex manifolds.

- Acta Scientiarum MathematicarumAvramov lecture: "... - Zentralblatt MATHValla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory."

The action of a compact Lie group, G, on a compact sympletic manifold gives rise to some remarkable combinatorial invariants. The simplest and most interesting of these is the moment polytopes, a convex polyhedron which sits inside the dual of the Lie algebra of G.

The book will be of interest to researchers in the fields of differential geometry, complex geometry, and several complex variables geometry, as well as to graduate students in mathematics.

This book takes the reader from the end of introductory Lie group theory to the threshold of infinite-dimensional group representations. Merging algebra and analysis throughout, the author uses Lie-theoretic methods to develop a beautiful theory having wide applications in mathematics and physics.

This book expresses the full understanding of Weyl's formula for the volume of a tube, its roots and its implications. Historical notes and Mathematica drawings have been added to this revised second edition. From the reviews:"Will do much to make Weyl's tube formula more accessible to modern readers....

"...A nice feature of the book [is] that at various points the authors provide examples, or rather counterexamples, that clearly show what can go wrong...This is a nicely-written book [that] studies algebraic differential modules in several variables."--Mathematical Reviews

Contains a significant amount of new in areas of interest, and presents the "big picture" in an engaging framework.

Suitable for researchers working in analysis in general, in harmonic analysis, or in mathematical physics.

Deals with the study of rational and integral points on higher-dimensional algebraic varieties. This book contains selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies.

Eisenstein series are an essential ingredient in the spectral theory of automorphic forms and an important tool in the theory of L-functions. Bringing together contributions from areas which do not usually interact with each other, this volume introduces diverse users of Eisenstein series to a variety of important applications.

And finally, the book presents some applications to evolution problems, index theory, fractional powers, spectral theory and singular perturbation theory.

Details the mathematical developments in total variation based image restauration. This book is devoted to PDE's of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a special emphasis on the applications related to image restoration and nonlinear filters.

This book gives an introduction to index theory for symplectic matrix paths and its iteration theory, as well as applications to periodic solution problems of nonlinear Hamiltonian systems.

An exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property?

Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin consists ofinvited expository and research articles on new developments arising fromManin's outstanding contributions to mathematics.

Algebra, Arithmetic, and Geometry: In Honor of Yu. I. Manin consists ofinvited expository and research articles on new developments arising fromManin's outstanding contributions to mathematics.

The main objective of this book is to give a broad uni?ed introduction to the study of dimension and recurrence inhyperbolic dynamics.

This text offers a collection of survey and research papers by leading specialists in the field documenting the current understanding of higher dimensional varieties.

The first European Congress of Mathematics was held in Paris from July 6 to July 10, 1992, at the Sorbonne and Pantheon-Sorbonne universities. Moreover, a Junior Mathematical Congress was organized, in parallel with the Congress, which brought together two hundred high school students.

Harmonic analysis and probability have long enjoyed a mutually beneficial relationship that has been rich and fruitful. This work explores several aspects of this relationship. It focuses on the nontangential maximal function and the area function of a harmonic function and their probabilistic analogues in martingale theory.

In the fall of 1992 I was invited by Professor Changho Keem to visit Seoul National University and give a series of talks.

The Radon transform is an important topic in integral geometry which deals with the problem of expressing a function on a manifold in terms of its integrals over certain submanifolds. Readers will find here an accessible introduction to Radon transform theory, an elegant topic in integral geometry.

Examples of such decidabLe theories are the theory of Boolean algebras (Tarski [1949]), the theory of Abelian groups (Szmiele~ [1955]), and the theories of elementary arithmetic and geometry (Tarski [1951]' but Tarski discovered these results around 1930).

Part I deals with the Hille--Yosida and Lumer--Phillips characterizations of semigroup generators, the Trotter--Kato approximation theorem, Kato's unified treatment of the exponential formula and the Trotter product formula, the Hille--Phillips perturbation theorem, and Stone's representation of unitary semigroups.

This volume provides an overview of rationality problems by surveying research from leading experts in the field. Readers will find coverage of rationality problems from both cohomological and algebraic geometry perspectives.

Then it is divided into three parts, each of them devoted to a speci?c subject studied by Gaeta and coordinated by one of the editors. For each part, we had the advice of another colleague of Federico linked to that particular subject, who also contributed with a short survey.

Ferran Sunyer i Balaguer Award winning monograph

The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups.Contributors: B.

Motivated by some notorious open problems, such as the Jacobian conjecture and the tame generators problem, the subject of polynomial automorphisms has become a rapidly growing field of interest.