Anton Zettl, Northern Illinois University, DeKalb, IL

Sturm-Liouville Theory

Expected publication date is October 9, 2005

Description

In 1836 and 1837, Sturm and Liouville published a series of papers on second order linear ordinary differential operators, which began the subject now known as the Sturm-Liouville theory. In 1910, Hermann Weyl published an article which started the study of singular Sturm-Liouville problems. Since then, Sturm-Liouville theory has remained an intensely active field of research with many applications in mathematics and mathematical physics.

The purpose of the present book is (a) to provide a modern survey of some of the basic properties of Sturm-Liouville theory and (b) to bring the reader to the forefront of research on some aspects of this theory. Prerequisites for using the book are a basic knowledge of advanced calculus and a rudimentary knowledge of Lebesgue integration and operator theory. The book has an extensive list of references and examples and numerous open problems. Examples includes classical equations and functions associated with Bessel, Fourier, Heun, Ince, Jacobi, Jorgens, Latzko, Legendre, Littlewood-McLeod, Mathieu, Meissner, and Morse; also included are examples associated with the harmonic oscillator and the hydrogen atom. Many special functions of applied mathematics and mathematical physics occur in these examples.

This book offers a well-organized viewpoint on some basic features of Sturm-Liouville theory. With many useful examples treated in detail, it will make a fine independent study text and is suitable for graduate students and researchers interested in differential equations.

Contents

Details:

Series: Mathematical Surveys and Monographs,Volume: 121
Publication Year: 2005
ISBN: 0-8218-3905-5
Paging: 328 pp.
Binding: Hardcover

D. Zhelobenko, Moscow, Russia

Principal Structures and Methods of Representation Theory

Expected publication date is September 25, 2005

Description

The main topic of this book can be described as the theory of algebraic and topological structures admitting natural representations by operators in vector spaces. These structures include topological algebras, Lie algebras, topological groups, and Lie groups.

The book is divided into three parts. Part I surveys general facts for beginners, including linear algebra and functional analysis. Part II considers associative algebras, Lie algebras, topological groups, and Lie groups, along with some aspects of ring theory and the theory of algebraic groups. The author provides a detailed account of classical results in related branches of mathematics, such as invariant integration and Lie's theory of connections between Lie groups and Lie algebras. Part III discusses semisimple Lie algebras and Lie groups, Banach algebras, and quantum groups.

This is a useful text for a wide range of specialists, including graduate students and researchers working in mathematical physics and specialists interested in modern representation theory. It is suitable for independent study or supplementary reading.

Also available from the AMS by this acclaimed author is Compact Lie Groups and Their Representations.

Contents

Details:

Series: Translations of Mathematical Monographs, Volume: 228
Publication Year: 2005
ISBN: 0-8218-3731-1
Paging: approximately 448 pp.
Binding: Hardcover

Henry P. McKean

Stochastic Integrals

Expected publication date is November 3, 2005

Description

The AMS is excited to bring this volume, originally published in 1969, back into print. This well-written book has been used for many years to learn about stochastic integrals.

The author starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Ito lemma. The rest of the book is devoted to various topics of stochastic integral equations and stochastic integral equations on smooth manifolds.

E. B. Dynkin wrote about the original edition in Mathematical Reviews: "This little book is a brilliant introduction to an important boundary field between the theory of probability and that of differential equations ... differential and integral calculus based upon Brownian motion." These words continue to ring true today.

This classic book is ideal for supplementary reading or independent study. It is suitable for graduate students and researchers interested in probability, stochastic processes, and their applications.

Contents

Details:

Series: AMS Chelsea Publishing Publication Year: 1969
Reprint/Revision History: first AMS printing 2005
ISBN: 0-8218-3887-3
Paging: 141 pp.
Binding: Hardcover

Edited by: B. Diarra and A. Escassut, Universite Blaise Pascal, Aubiere, France, A. K. Katsaras, University of Ioannina, Greece, and L. Narici, St. John's University, Jamaica, NY

Ultrametric Functional Analysis

Expected publication date is October 16, 2005

Description

With contributions by leading mathematicians, this proceedings volume reflects the program of the Eighth International Conference on p-adic Functional Analysis held at Blaise Pascal University (Clermont-Ferrand, France).

Articles in the book offer a comprehensive overview of research in the area. A wide range of topics are covered, including basic ultrametric functional analysis, topological vector spaces, measure and integration, Choquet theory, Banach and topological algebras, analytic functions (in particular, in connection with algebraic geometry), roots of rational functions and Frobenius structure in p-adic differential equations, and q-ultrametric calculus.

The material is suitable for graduate students and researchers interested in number theory, functional analysis, and algebra.

Contents

J. Aguayo -- Vector measures and integral operators in the nonarchimedean setting
J. Aguayo, A. K. Katsaras, and S. Navarro -- On the dual space for the strict topology beta_1 and the space M(X) in function space
J. Aguayo, J. Gomez, M. Saavedra, and M. Wallace -- Perturbation of a p-adic dynamical system in two variables
J. Araujo -- Isomorphisms with small bound between spaces of p-adic continuous functions II
B. Diarra -- Ultrametric q-calculus
N. De Grande-De Kimpe and C. Perez-Garcia -- Strictness and closedness in p-adic inductive limits
P.-C. Hu and C.-C. Yang -- A note on Browkin-Brzezinski conjecture
A. K. Katsaras -- Non-Archimedean integration and strict topologies
H. A. Keller and H. O. A. -- Non-Archimedean orthomodular spaces and their residual spaces
A. N. Kochubei -- Polylogarithms and a zeta function for finite places of a function field
A. Kubzdela -- On finite-dimensional normed spaces over C_p
L. Narici and E. Beckenstein -- A non-Archimedean inner product
H. Ochsenius and W. H. Schikhof -- Lipschitz operators on Banach spaces over Krull valued fields
S. Priess-Crampe -- Remarks on some theorems of functional analysis
A. Pulita -- Frobenius structure for rank one p-adic differential equations
A. Salinier -- The ultrametric spectrum as an ordered set
M.-C. Sarmant -- Analytic roots of rational functions whose poles are on the unit circle
W. H. Schikhof -- p-adic Choquet theory
E. Schorner -- The spherical completion of normed vector spaces over fields with valuations of arbitrary rank
W. Sliwa -- On Kothe quotients of non-Archimedean Frechet spaces
T. H. H. An and J. T.-Y. Wang -- Unique range sets for non-Archimedean entire functions in positive characteristic fields
F. Tangara -- Some continuous linear operators and orthogonal q-bases on the space of p-adic continuous functions defined on mathbb{Z}_p
J. T.-Y. Wang -- Uniqueness polynomials, unique range sets and other uniqueness theorems

Details:

Series: Contemporary Mathematics,Volume: 384
Publication Year: 2005
ISBN: 0-8218-3684-6
Paging: 369 pp.
Binding: Softcover

Christian Meyer, Johannes Gutenberg University, Mainz, Germany

Modular Calabi-Yau Threefolds

Expected publication date is November 3, 2005

Description

This book discusses the connection between Calabi-Yau threefolds and modular forms. It presents the general theory and brings together the known results. Hundreds of new examples are given of rigid and non-rigid Calabi-Yau threefolds, and the construction of correspondences between them leads to conjectures about the modular forms involved. The author has compiled tables of newforms of weight four and large levels, which are included in the appendix.

The great variety of new examples as well as the tables of newforms makes this volume a valuable resource for graduate students and researchers interested in algebraic geometry and arithmetic algebraic geometry.

Contents

Details:

Series: Fields Institute Monographs, Volume: 22
Publication Year: 2005
ISBN: 0-8218-3908-X
Paging: 194 pp.
Binding: Hardcover