Tube Domains and the Cauchy Problem
Tube Domains and the Cauchy Problem

Author: Semen Grigorʹevich Gindikin

Publisher: American Mathematical Soc.

Published:

Total Pages: 144

ISBN-13: 9780821897409

DOWNLOAD EBOOK

This book is dedicated to two problems. The first concerns the description of maximal exponential growth of functions or distributions for which the Cauchy problem is well posed. The descriptions presented in the language of the behaviour of the symbol in a complex domain. The second problem concerns the structure of and explicit formulas for differential operators with large automorphism groups. It is suitable as an advanced graduate text in courses in partial differential equations and the theory of distributions.

Embeddings and Immersions
Embeddings and Immersions

Author: Masahisa Adachi

Publisher: American Mathematical Soc.

Published: 2012-11-07

Total Pages: 198

ISBN-13: 0821891642

DOWNLOAD EBOOK

This book covers fundamental techniques in the theory of -imbeddings and -immersions, emphasizing clear intuitive understanding and containing many figures and diagrams. Adachi starts with an introduction to the work of Whitney and of Haefliger on -imbeddings and -manifolds. The Smale-Hirsch theorem is presented as a generalization of the classification of -imbeddings by isotopy and is extended by Gromov's work on the subject, including Gromov's convex integration theory. Finally, as an application of Gromov's work, the author introduces Haefliger's classification theorem of foliations on open manifolds. Also described here is the Adachi's work with Landweber on the integrability of almost complex structures on open manifolds. This book would be an excellent text for upper-division undergraduate or graduate courses.Nothing provided

Mathematics of Fractals
Mathematics of Fractals

Author: Masaya Yamaguchi

Publisher: American Mathematical Soc.

Published: 1997

Total Pages: 104

ISBN-13: 9780821805374

DOWNLOAD EBOOK

This book aims at providing a handy explanation of the notions behind the self-similar sets called "fractals" and "chaotic dynamical systems". The authors emphasize the beautiful relationship between fractal functions (such as Weierstrass's) and chaotic dynamical systems; these nowhere-differentiable functions are generating functions of chaotic dynamical systems. These functions are shown to be in a sense unique solutions of certain boundary problems. The last chapter of the book treats harmonic functions on fractal sets.

Infinite-Dimensional Lie Groups
Infinite-Dimensional Lie Groups

Author: Hideki Omori

Publisher: American Mathematical Soc.

Published: 2017-11-07

Total Pages: 434

ISBN-13: 1470426358

DOWNLOAD EBOOK

This book develops, from the viewpoint of abstract group theory, a general theory of infinite-dimensional Lie groups involving the implicit function theorem and the Frobenius theorem. Omori treats as infinite-dimensional Lie groups all the real, primitive, infinite transformation groups studied by E. Cartan. The book discusses several noncommutative algebras such as Weyl algebras and algebras of quantum groups and their automorphism groups. The notion of a noncommutative manifold is described, and the deformation quantization of certain algebras is discussed from the viewpoint of Lie algebras. This edition is a revised version of the book of the same title published in Japanese in 1979.

Linear and Nonlinear Perturbations of the Operator Div
Linear and Nonlinear Perturbations of the Operator Div

Author: Viktor Grigorʹevich Osmolovskiĭ

Publisher: American Mathematical Soc.

Published: 1997-01-01

Total Pages: 126

ISBN-13: 9780821897744

DOWNLOAD EBOOK

This book presents results onboundary-value problems for L and the theory of nonlinear perturbations of L. Specifically, necessary and sufficient solvability conditions in explicit form are found for various boundary-value problems for the operator L. an analog of the Weyl decomposition is proved.

Introduction to Complex Analysis
Introduction to Complex Analysis

Author: Junjiro Noguchi

Publisher: American Mathematical Soc.

Published: 2008-04-09

Total Pages: 268

ISBN-13: 9780821889602

DOWNLOAD EBOOK

This book describes a classical introductory part of complex analysis for university students in the sciences and engineering and could serve as a text or reference book. It places emphasis on rigorous proofs, presenting the subject as a fundamental mathematical theory. The volume begins with a problem dealing with curves related to Cauchy's integral theorem. To deal with it rigorously, the author gives detailed descriptions of the homotopy of plane curves. Since the residue theorem is important in both pure and applied mathematics, the author gives a fairly detailed explanation of how to apply it to numerical calculations; this should be sufficient for those who are studying complex analysis as a tool.

Tangents and Secants of Algebraic Varieties
Tangents and Secants of Algebraic Varieties

Author: F. L. Zak

Publisher: American Mathematical Soc.

Published: 1993

Total Pages: 176

ISBN-13: 0821838377

DOWNLOAD EBOOK

"The book is devoted to geometry of algebraic varieties in projective spaces. Among the objects considered in some detail are tangent and secant varieties, Gauss maps, dual varieties, hyperplane sections, projections, and varieties of small codimension. Emphasis is made on the study of interplay between irregular behavior of (higher) secant varieties and irregular tangencies to the original variety. Classification of varieties with unusual tangential properties yields interesting examples many of which arise as orbits of representations of algebraic groups."--ABSTRACT.

Complements of Discriminants of Smooth Maps
Complements of Discriminants of Smooth Maps

Author: V. A. Vasilʹev

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 282

ISBN-13: 9780821898376

DOWNLOAD EBOOK

* Up-to-date reference on this exciting area of mathematics * Discusses the wide range of applications in topology, algebraic geometry, and catastrophe theory.

An Introduction to Sato's Hyperfunctions
An Introduction to Sato's Hyperfunctions

Author: Mitsuo Morimoto

Publisher: American Mathematical Soc.

Published: 1993-01-01

Total Pages: 292

ISBN-13: 9780821887677

DOWNLOAD EBOOK

This book is a translation, with corrections and an updated bibliography, of Morimoto's 1976 book on the theory of hyperfunctions originally written in Japanese. Since the time that Sato established the theory of hyperfunctions, there have been many important applications to such areas as pseudodifferential operators and S-matrices. Assuming as little background as possible on the part of the reader, Morimoto covers the basic notions of the theory, from hyperfunctions of one variable to Sato's fundamental theorem. This book provides an excellent introduction to this important field of research.