Bücher der Reihe Progress in Mathematics

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.

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

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.

This second edition, divided into fourteen chapters, presents a comprehensive treatment of contact and symplectic manifolds from the Riemannian point of view.

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.

This book provides the proof of a complex geometric version of a well-known result in algebraic geometry: the theorem of Riemann-Roch-Grothendieck for proper submersions. It gives an equality of cohomology classes in Bott-Chern cohomology.

From the reviews: "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds." -Zentralblatt Math"This monograph contains a wealth of information many topologists will find very handy.

Key topics discussed include spherical varieties, Littelmann Paths and Kac-Moody Lie algebras, modular representations, primitive ideals, representation theory of Artin algebras and quivers, Kac-Moody superalgebras, categories of Harish-Chandra modules, cohomological methods, and cluster algebras.

This is a collection of research-oriented monographs, reports, and notes arising from lectures and seminars on the Weil representation, the Maslov index, and the Theta series. It is good contribution to the international scientific community, particularly for researchers and graduate students in the field.

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

In the 1970s Hirzebruch and Zagier produced elliptic modular forms with coefficients in the homology of a Hilbert modular surface. They then computed the Fourier coefficients of these forms in terms of period integrals and L-functions. In this book the authors take an alternate approach to these theorems and generalize them to the setting of Hilbert modular varieties of arbitrary dimension. The approach is conceptual and uses tools that were not available to Hirzebruch and Zagier, including intersection homology theory, properties of modular cycles, and base change. Automorphic vector bundles, Hecke operators and Fourier coefficients of modular forms are presented both in the classical and adelic settings. The book should provide a foundation for approaching similar questions for other locally symmetric spaces.

. . . . . . . . . . . . . . . . . . . . . . . . Some Aspects of Homological Algebra . Endomorphism Rings . 87 Bibliography . , 91 LATTICE THEORY M. Boolean Algebras . " 111 2. Identity and Defining Relations in Lattices . * . * . Lattices of Congruences and of Ideals of a Lattice . Closure Operators . Drinfel'd Preface .

This Lecture Notes volume is the fruit of two research-level summer schools jointly organized by the GTEM node at Lille University and the team of Galatasaray University (Istanbul): "Geometry and Arithmetic of Moduli Spaces of Coverings (2008)" and "Geometry and Arithmetic around Galois Theory (2009)".

This book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and the integrability of complex analytical linear differential equations. For linear differential equations, integrability is made precise within the framework of differential Galois theory. The connection of these two integrability notions is given by the variational equation (i.e. linearized equation) along a particular integral curve of the Hamiltonian system. The underlying heuristic idea, which motivated the main results presented in this monograph, is that a necessary condition for the integrability of a Hamiltonian system is the integrability of the variational equation along any of its particular integral curves. This idea led to the algebraic non-integrability criteria for Hamiltonian systems. These criteria can be considered as generalizations of classical non-integrability results by Poincare and Liapunov, as well as more recent results by Ziglin and Yoshida. Thus, by means of the differential Galois theory it is not only possible to understand all these approaches in a unified way but also to improve them. Several important applications are also included: homogeneous potentials, Bianchi IX cosmological model, three-body problem, Henon-Heiles system, etc.The book is based on the original joint research of the author with J.M. Peris, J.P. Ramis and C. Simo, but an effort was made to present these achievements in their logical order rather than their historical one. The necessary background on differential Galois theory and Hamiltonian systems is included, and several new problems and conjectures which open new lines of research are proposed.

Rational Homotopy Theory and Differential Forms

Foundations of the Theory of Categories . Fundamentals of the Theory of Categories . Embeddings of Categories ... Representations of Categories . Axiomatic Characteristics of Algebraic Categories . Radicals in Categories . Universal Algebras in Categories . Categories with Multiplication . Concrete Categories .

Ideals e) Exterior Differential Systems EULER-LAGRANGE EQUATIONS FOR DIFFERENTIAL SYSTEMS ~liTH ONE I. Classical Examples b) Variational Equations for Integral Manifolds of Differential Systems c) Differential Systems in Good Form; iii) the Genera 1 Euler Equations 2 K /2 ds b) Examples: i) the Euler Equations Associated to f for lEn;

Chance-Constrained Problems . Rigorous Statement of stochastic Linear Programming Problems . Nonrigorous Statement of SLP Problems . Existence of Domains of Stability of the Solutions of SLP Problems . Some Algorithms for the Solution of Stochastic Linear Programming Problems . Stochastic Nonlinear Programming: Some First Results .

The third article reflects the present state of the art in the given area of the theory of representations, which has been re ceiving considerable attention in connection with its applications in physics (particularly in quantum field theory) and in the theory of differential equations.

For about a decade I have made an effort to study quadratic forms in infinite dimensional vector spaces over arbitrary division rings. If one wants to give an introduction to the geometric algebra of infinite dimensional quadratic spaces, a discussion of N-dimensional O spaces ideally serves the purpose.

Let N be prime, and be a weight two newform for r 0 (N) . For a primitive Dirichlet character X of conductor prime to N, let i\ f (X) denote the algebraic part of L (f , X, 1) (see below). Mazur's congruence formulae were extended to r 1 (N), N prime, by S.

These lecture notes are intended as an introduction to the methods of classification of holomorphic vector bundles over projective algebraic manifolds X. According to Serre (GAGA) the classification of holomorphic vector bundles is equivalent to the classification of algebraic vector bundles.

The first edition of this book has been out of print for some time and I have decided to follow the publisher's kind suggestion to prepare a new edition. Here 5 provides proofs of the needed results about the Riesz potentials while 3-4 develop the tools from Fourier analysis following closely the account in Hormander's books (1963] and [1983].