Some Properties Of Differentiable Varieties And Transformations
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Some Properties Of Differentiable Varieties And Transformations
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Author : Beniamino Segre
language : en
Publisher: Springer
Release Date : 2012-12-06
Some Properties Of Differentiable Varieties And Transformations written by Beniamino Segre and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The present volume contains, together with numerous additions and extensions, the course of lectures which I gave at Pavia (26 September till 5 October 1955) by invitation of the «Centro Internazionale Mate matico Estivo». The treatment has the character of a monograph, and presents various novel features, both in form and in substance; these are indicated in the notes which will be found at the beginning and end of each chapter. Of the nine parts into which the work is divided, the first four are essentially differential in character, the next three deal with algebraic geometry, while the last two are concerned with certain aspects of the theory of differential equations and of correspondences between topo logical varieties. A glance at the index will suffice to give a more exact idea of the range and variety of the contents, whose chief characteristic is that of establishing suggestive and sometimes unforeseen relations between apparently diverse subjects (e. g. differential geometry in the small and also in the large, algebraic geometry, function theory, topo logy, etc.); prominence is given throughout to the geometrical viewpoint, and tedious calculations are as far as possible avoided.
Integration In Hilbert Space
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Author : A. V. Skorohod
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integration In Hilbert Space written by A. V. Skorohod and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Integration in function spaces arose in probability theory when a gen eral theory of random processes was constructed. Here credit is cer tainly due to N. Wiener, who constructed a measure in function space, integrals-with respect to which express the mean value of functionals of Brownian motion trajectories. Brownian trajectories had previously been considered as merely physical (rather than mathematical) phe nomena. A. N. Kolmogorov generalized Wiener's construction to allow one to establish the existence of a measure corresponding to an arbitrary random process. These investigations were the beginning of the development of the theory of stochastic processes. A considerable part of this theory involves the solution of problems in the theory of measures on function spaces in the specific language of stochastic pro cesses. For example, finding the properties of sample functions is connected with the problem of the existence of a measure on some space; certain problems in statisticsreduce to the calculation of the density of one measure w. r. t. another one, and the study of transformations of random processes leads to the study of transformations of function spaces with measure. One must note that the language of probability theory tends to obscure the results obtained in these areas for mathematicians working in other fields. Another dir,ection leading to the study of integrals in function space is the theory and application of differential equations. A. N.
Jordan Algebras And Algebraic Groups
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Author : Tonny A. Springer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Jordan Algebras And Algebraic Groups written by Tonny A. Springer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From the reviews: "This book presents an important and novel approach to Jordan algebras. Jordan algebras have come to play a role in many areas of mathematics, including Lie algebras and the geometry of Chevalley groups. Springer's work will be of service to research workers familiar with linear algebraic groups who find they need to know something about Jordan algebras and will provide Jordan algebraists with new techniques and a new approach to finite-dimensional algebras over fields." (American Scientist) "By placing the classification of Jordan algebras in the perspective of classification of certain root systems, the book demonstrates that the structure theories associative, Lie, and Jordan algebras are not separate creations but rather instances of the one all-encompassing miracle of root systems. ..." (Math. Reviews)
Topics In M Adic Topologies
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Author : Silvio Greco
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Topics In M Adic Topologies written by Silvio Greco and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The m-adic topologies and, in particular the notions of m-complete ring and m-completion A of a commutative ring A, occur frequently in commutative algebra and are also a useful tool in algebraic geometry. The aim of this work is to collect together some criteria concerning the ascent (from A to A) and the descent (from A to A) of several properties of commutative rings such as, for example: integrity, regularity, factoriality, normality, etc. More precisely, we want to show that many of the above criteria, although not trivial at all, are elementary consequences of some fundamental notions of commutative algebra and local algebra. Sometimes we are able to get only partial results, which probably can be improved by further deeper investigations. No new result has been included in this work. Its only origi nality is the choice of material and the mode of presentation. The comprehension of the most important statements included in this book needs only a very elementary background in algebra, ideal theory and general topology. In order to emphasize the elementary character of our treatment, we have recalled several well known definitions and, sometimes, even the proofs of the first properties which follow directly from them. On the other hand, we did not insert in this work some important results, such as the Cohen structure theorem on complete noetherian local rings, as we did not want to get away too much from the spirit of the book.
Harmonic Analysis Of Spherical Functions On Real Reductive Groups
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Author : Ramesh Gangolli
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Harmonic Analysis Of Spherical Functions On Real Reductive Groups written by Ramesh Gangolli and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Analysis on Symmetric spaces, or more generally, on homogeneous spaces of semisimple Lie groups, is a subject that has undergone a vigorous development in recent years, and has become a central part of contemporary mathematics. This is only to be expected, since homogeneous spaces and group representations arise naturally in diverse contexts ranging from Number theory and Geometry to Particle Physics and Polymer Chemistry. Its explosive growth sometimes makes it difficult to realize that it is actually relatively young as mathematical theories go. The early ideas in the subject (as is the case with many others) go back to Elie Cart an and Hermann Weyl who studied the compact symmetric spaces in the 1930's. However its full development did not begin until the 1950's when Gel'fand and Harish Chandra dared to dream of a theory of representations that included all semisimple Lie groups. Harish-Chandra's theory of spherical functions was essentially complete in the late 1950's, and was to prove to be the forerunner of his monumental work on harmonic analysis on reductive groups that has inspired a whole generation of mathematicians. It is the harmonic analysis of spherical functions on symmetric spaces, that is at the focus of this book. The fundamental questions of harmonic analysis on symmetric spaces involve an interplay of the geometric, analytical, and algebraic aspects of these spaces. They have therefore attracted a great deal of attention, and there have been many excellent expositions of the themes that are characteristic of this subject.
Inequalities
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Author : Edwin F. Beckenbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Inequalities written by Edwin F. Beckenbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Since the elassie work on inequalities by HARDY, LITTLEWOOD, and P6LYA in 1934, an enonnous amount of effort has been devoted to the sharpening and extension of the elassieal inequalities, to the discovery of new types of inequalities, and to the application of inqualities in many parts of analysis. As examples, let us eite the fields of ordinary and partial differential equations, whieh are dominated by inequalities and variational prineiples involving functions and their derivatives; the many applications of linear inequalities to game theory and mathe matieal economics, which have triggered a renewed interest in con vexity and moment-space theory; and the growing uses of digital com puters, which have given impetus to a systematie study of error esti mates involving much sophisticated matrix theory and operator theory. The results presented in the following pages reflect to some extent these ramifications of inequalities into contiguous regions of analysis, but to a greater extent our concem is with inequalities in their native habitat. Since it is elearly impossible to give a connected account of the burst of analytic activity of the last twenty-five years centering about inequalities, we have d. eeided to limit our attention to those topies that have particularly delighted and intrigued us, and to the study of whieh we have contributed.
Compact Convex Sets And Boundary Integrals
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Author : Erik M. Alfsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Compact Convex Sets And Boundary Integrals written by Erik M. Alfsen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The importance of convexity arguments in functional analysis has long been realized, but a comprehensive theory of infinite-dimensional convex sets has hardly existed for more than a decade. In fact, the integral representation theorems of Choquet and Bishop -de Leeuw together with the uniqueness theorem of Choquet inaugurated a new epoch in infinite-dimensional convexity. Initially considered curious and tech nically difficult, these theorems attracted many mathematicians, and the proofs were gradually simplified and fitted into a general theory. The results can no longer be considered very "deep" or difficult, but they certainly remain all the more important. Today Choquet Theory provides a unified approach to integral representations in fields as diverse as potential theory, probability, function algebras, operator theory, group representations and ergodic theory. At the same time the new concepts and results have made it possible, and relevant, to ask new questions within the abstract theory itself. Such questions pertain to the interplay between compact convex sets K and their associated spaces A(K) of continuous affine functions; to the duality between faces of K and appropriate ideals of A(K); to dominated extension problems for continuous affine functions on faces; and to direct convex sum decomposition into faces, as well as to integral for mulas generalizing such decompositions. These problems are of geometric interest in their own right, but they are primarily suggested by applica tions, in particular to operator theory and function algebras.
Finiteness Conditions And Generalized Soluble Groups
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Author : Derek J.S. Robinson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Finiteness Conditions And Generalized Soluble Groups written by Derek J.S. Robinson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This book is a study of group theoretical properties of two disparate kinds, firstly finiteness conditions or generalizations of finiteness and secondly generalizations of solubility or nilpotence. It will be particularly interesting to discuss groups which possess properties of both types. The origins of the subject may be traced back to the nineteen twenties and thirties and are associated with the names of R. Baer, S.N. Cernikov, K.A. Hirsch, A.G. Kuros, 0.]. Schmidt and H. Wielandt. Since this early period, the body of theory has expanded at an increasingly rapid rate through the efforts of many group theorists, particularly in Germany, Great Britain and the Soviet Union. Some of the highest points attained can, perhaps, be found in the work of P. Hall and A.I. Mal'cev on infinite soluble groups. Kuras's well-known book "The theory of groups" has exercised a strong influence on the development of the theory of infinite groups: this is particularly true of the second edition in its English translation of 1955. To cope with the enormous increase in knowledge since that date, a third volume, containing a survey of the contents of a very large number of papers but without proofs, was added to the book in 1967
Indefinite Inner Product Spaces
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Author : J. Bognar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Indefinite Inner Product Spaces written by J. Bognar and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
By definition, an indefinite inner product space is a real or complex vector space together with a symmetric (in the complex case: hermi tian) bilinear form prescribed on it so that the corresponding quadratic form assumes both positive and negative values. The most important special case arises when a Hilbert space is considered as an orthogonal direct sum of two subspaces, one equipped with the original inner prod uct, and the other with -1 times the original inner product. The subject first appeared thirty years ago in a paper of Dirac [1] on quantum field theory (d. also Pauli [lJ). Soon afterwards, Pontrja gin [1] gave the first mathematical treatment of an indefinite inner prod uct space. Pontrjagin was unaware of the investigations of Dirac and Pauli; on the other hand, he was inspired by a work of Sobolev [lJ, unpublished up to 1960, concerning a problem of mechanics. The attempts of Dirac and Pauli to apply the concept and elemen tary properties of indefinite inner product spaces to field theory have been renewed by several authors. At present it is not easy to judge which of their results will contribute to the final form of this part of physics. The following list of references should serve as a guide to the extensive literature: Bleuler [1], Gupta [lJ, Kallen and Pauli [lJ, Heisen berg [lJ-[4J, Bogoljubov, Medvedev and Polivanov [lJ, K.L. Nagy [lJ-[3], Berezin [lJ, Arons, Han and Sudarshan [1], Lee and Wick [1J.
Modular Lie Algebras
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Author : Geoge B. Seligman
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Modular Lie Algebras written by Geoge B. Seligman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The study of the structure of Lie algebras over arbitrary fields is now a little more than thirty years old. The first papers, to my know ledge, which undertook this study as an end in itself were those of JACOBSON (" Rational methods in the theory of Lie algebras ") in the Annals, and of LANDHERR ("Uber einfache Liesche Ringe") in the Hamburg Abhandlungen, both in 1935. Over fields of characteristic zero, these thirty years have seen the ideas and results inherited from LIE, KILLING, E. CARTAN and WEYL developed and given new depth, meaning and elegance by many contributors. Much of this work is presented in [47, 64, 128 and 234] of the bibliography. For those who find the rationalization for the study of Lie algebras in their connections with Lie groups, satisfying counterparts to these connections have been found over general non-modular fields, with the substitution of the formal groups of BOCHNER [40] (see also DIEUDONNE [108]), or that of the algebraic linear groups of CHEVALLEY [71], for the usual Lie group. In particular, the relation with algebraic linear groups has stimulated the study of Lie algebras of linear transformations. When one admits to consideration Lie algebras over a base field of positive characteristic (such are the algebras to which the title of this monograph refers), he encounters a new and initially confusing scene.