Series: Cambridge Tracts in Mathematics (No. 183)
Hardback (ISBN-13: 9780521197694)
Page extent: 400 pages
Size: 228 x 152 mm
This book is, on the one hand, a pedagogical introduction to the formalism of slopes, of semi-stability and of related concepts in the simplest possible context. It is therefore accessible to any graduate student with a basic knowledge in algebraic geometry and algebraic groups. On the other hand, the book also provides a thorough introduction to the basics of period domains, as they appear in the geometric approach to local Langlands correspondences and in the recent conjectural p-adic local Langlands program. The authors provide numerous worked examples and establish many connections to topics in the general area of algebraic groups over finite and local fields. In addition, the end of each section includes remarks on open questions, historical context and references to the literature.
* Contains complete proofs of the basics of the theory * Brings together tools from various branches of algebra and geometry * Provides a basis for future research
Contents
Preface; Introduction; Part I. Period Domains for GLn Over a Finite Field: 1. Filtered vector spaces; 2. Period domains for GLn; 3. Cohomology of period domains for GLn; Part II. Period Domains for Reductive Groups over Finite Fields: 4. Interlude on the Tannakian formalism; 5. Filtrations on repk(G); 6. Period domains for reductive groups; 7. Cohomology of period domains for reductive groups; Part III. Period Domains over p-adic Fields: 8. Period domains over p-adic fields; 9. Period domains for p-adic reductive groups; 10. Cohomology of period domains over p-adic fields; Part IV. Complements: 11. Further aspects of period domains; References; Index.
Series: Cambridge Studies in Advanced Mathematics (No. 126)
Hardback (ISBN-13: 9780521197977)
3 b/w illus. 350 exercises
Page extent: 450 pages
Size: 228 x 152 mm
The subject of special functions is often presented as a collection of disparate results, which are rarely organised in a coherent way. This book answers the need for a different approach to the subject. The authors' main goals are to emphasise general unifying principles coherently and to provide clear motivation, efficient proofs, and original references for all of the principal results. The book covers standard material, but also much more, including chapters on discrete orthogonal polynomials and elliptic functions. The authors show how a very large part of the subject traces back to two equations - the hypergeometric equation and the confluent hypergeometric equation - and describe the various ways in which these equations are canonical and special. Providing ready access to theory and formulas, this book serves as an ideal graduate-level textbook as well as a convenient reference.
* Unified view provides a framework that allows students a firmer grasp of the material * Brief appendices outline material from complex analysis and Fourier analysis * Includes succinct end-of-chapter summaries and over 350 exercises
Preface; 1. Orientation; 2. Gamma, beta, zeta; 3. Second order differential equations; 4. Orthogonal polynomials; 5. Discrete orthogonal polynomials; 6. Confluent hypergeometric functions; 7. Cylinder functions; 8. Hypergeometric functions; 9. Spherical functions; 10. Asymptotics; 11. Elliptic functions; References; Index.
ESI Lectures in Mathematics and Physics
ISBN 978-3-03719-076-0
DOI 10.4171/076
February 2010, 214 pages, softcover, 17 x 24 cm.
This book provides a thorough and self-contained introduction to the ∂-Neumann problem, leading up to current research, in the context of the *2-Sobolev theory on bounded pseudoconvex domains in *n. It grew out of courses for advanced graduate students and young researchers given by the author at the Erwin Schrodinger International Institute for Mathematical Physics and at Texas A&M University.
The introductory chapter provides an overview of the contents and puts them in historical perspective. The second chapter presents the basic *2-theory. Following is a chapter on the subelliptic estimates on strictly pseudoconvex domains. The two final chapters on compactness and on regularity in Sobolev spaces bring the reader to the frontiers of research.
Prerequisites are a solid background in basic complex and functional analysis, including the elementary *2-Sobolev theory and distributions. Some knowledge in several complex variables is helpful. Concerning partial differential equations, not much is assumed. The elliptic regularity of the Dirichlet problem for the Laplacian is quoted a few times, but the ellipticity results needed for elliptic regularization in the third chapter are proved from scratch.
The 3rd Lehmann Symposium was held in May 2007. The papers presented int his volume cover several areas: some of the works consider classical aspects of the discipline and others deal with contemporary aspects of the theory and applications of statistics. Thus, the reader will find a fascinating section dedicated to the subject of optimality. Lehmann, Bahadur and Bickel, and Huber provide excellent discussions on various aspects of optimality. Semi-parametric and non-parametric inference, bootstrap tests of hypotheses, functional data analysis, asymptotic theory, ad-hoc networks, and finance are some of the areas represented in the volume. It has been a goal of the Symposium to have a probability component.
the IMS Lecture Notes-Monographs Series vol.57
ISBN 978094060077