Bøger i Classics in Mathematics serien

From the reviews: "...a fine book [...] When it appeared in 1949 it was a pioneer. But Hasse has something extra to offer.[...] Hasse proved that miracles do happen in his five beautiful papers on quadratic forms of 1923-1924. [...]It is trite but true: Every number-theorist should have this book on his or her shelf."

, from Chapter IX (Analytical Theory of Semi-groups) directly to Chapter XIII (Ergodic Theory and Diffusion Theory) and to Chapter XIV (Integration of the Equation of Evolution).

Springer is reissuing a selected few highly successful books in a new, inexpensive softcover edition to make them easily accessible to younger generations of students and researchers. Springer-Verlag began publishing books in higher mathematics in 1920. This is a reprint of the Second Edition.

From the reviews: "[...] An excellent textbook in the theory of linear operators in Banach and Hilbert spaces. It is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.

From the reviews: "This book is an excellent presentation of the application of martingale theory to the theory of Markov processes, especially multidimensional diffusions. [...] This monograph can be recommended to graduate students and research workers but also to all interested in Markov processes from a more theoretical point of view."

Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties).

Volumes III and IV complete this treatise on linear partial differential equations. They constitute the most complete and up-to-date account of this subject by the author who has dominated it and made the most significant contributions in the last decades.

Peter Dembowski was born in Berlin on April 1, 1928. Dembowski taught at the universities of Frankfurt and Tuebingen and - as visiting Professor - in London (Queen Mary College), Rome, and Madison, WI.

Given a mathematical structure, one of the basic associated mathematical objects is its automorphism group. Chapter I describes a general theory of automorphisms of geometric structures with emphasis on the question of when the automorphism group can be given a Lie group structure.

From the Reviews: "To call this work encyclopedic would not give an accurate picture of its content and style. Some parts read like a textbook, but others are more technical and contain relatively new results. The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing."

however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy classes of maps and homotopy groups.Thus this book might be regarded as a fairly self-contained introduction to a "generalized cohomology theory".

Hestenes in Journal of Optimization Theory and Applications"The work intertwines in masterly fashion results of classical analysis, topology, and the theory of manifolds and thus presents a comprehensive treatise of the theory of multiple integral variational problems."L.

The prerequisites are minimal-just the standard graduate introduction to real analysis, complex analysis (one variable), and functional analysis. ...Mathematics lives in the book: main ideas of theorems and proofs, essential features of the subjects, lines of further developments, problems and conjectures are continually underlined.

This is the first book which presents an overview of several striking results ensuing from the examination of Einstein's equations in the context of Riemannian manifolds. Parts of the text can be used as an introduction to modern Riemannian geometry through topics like homogeneous spaces, submersions, or Riemannian functionals.

This work presents the theory of stochastic processes in its present state of rich imperfection. The exposition is robust and explicit, as one has come to expect of the Russian tradition of mathematical writing. The authors' display mastery of their material, and demonstrate their confident insight into its underlying structure.

Part of a treatise on linear partial differential equations, this title is useful for anybody interested in the theory of partial differential operators.

The main characteristic of this classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory.

This text examines the field of homology.

The main change in this edition is the inclusion of exercises with answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund.

From the reviews: "... Each chapter of the book is followed by a notes section and by a problems section. There are over 100 problems, many of which have hints. The book may be recommended as a text, it provides a completly self-contained reading ..." --S. Pogosian in Zentralblatt fur Mathematik

From the reviews "This book presents a complete treatment of a new class of random processes, which have been studied intensively during the last fifteen years. None of this material has ever appeared in book form before. The high quality of this work [...] makes a fascinating subject and its open problem as accessible as possible."

Author received the 1962 Fields MedalAuthor received the 1988 Wolf Prize (honoring achievemnets of a lifetime)Author is leading expert in partial differential equations

From the reviews: "Anyone who has heard O'Meara lecture will recognize in every page of this book the crispness and lucidity of the author's style. [...] The organization and selection of material is superb. [...] deserves high praise as an excellent example of that too-rare type of mathematical exposition combining conciseness with clarity."

Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena.

From the reviews: "A well-written, very thorough account ... Among the topics are lattices, reduction, Minkowskis Theorem, distance functions, packings, and automorphs; some applications to number theory; excellent bibliographical references." The American Mathematical Monthly

From the reviews: "The author's book [...] saw its first edition in 1935. [...] Now as before, the original text of the book is an excellent source for an interested reader to study the methods of classical algebraic geometry, and to find the great old results. [...] a timelessly beautiful pearl in the cultural heritage of mathematics as a whole."

It was meant to serve a double purpose: to help both, the student when first confronted with quantum mechanics and the experimental scientist, who has never before used it as a tool, to learn how to apply the general theory to practical problems of atomic physics.

From the reviews: "This book is an excellent and comprehensive survey of the theory of von Neumann algebras. It includes all the fundamental results of the subject, and is a valuable reference for both the beginner and the expert." Mathematical Reviews

From the reviews: "Theory of Stein Spaces provides a rich variety of methods, results, and motivations - a book with masterful mathematical care and judgement. It is a pleasure to have this fundamental material now readily accessible to any serious mathematician." --J. Eells in Bulletin of the London Mathematical Society (1980)

From the reviews: "Although several textbooks on modern algebraic geometry have been published in the meantime, Mumford's "Volume I" is, together with its predecessor the red book of varieties and schemes, now as before one of the most excellent and profound primers of modern algebraic geometry. Both books are just true classics!"