Schwartz Spaces, Nuclear Spaces and Tensor Products PDF Download

Author: Y.-C. Wong
Publisher: Springer
ISBN: 3540351612
Category : Mathematics
Languages : en
Pages : 426

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Author: David A.J. Seargent
Publisher: Springer
ISBN: 9780387095134
Category : Science
Languages : en
Pages : 260

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Naked-eye comets are far from uncommon. As a rough average, one appears every 18 months or thereabouts, and it is not very unusual to see more than two in a single year. The record so far seems to have been 2004, with a total of five comets visible without optical aid. But 2006, 1970, and 1911 were not far behind with a total of four apiece. Yet, the majority of these pass unnoticed by the general public. Most simply look like fuzzy stars with tails that are either faint or below the naked-eye threshold. The ‘classical’ comet – a bright star-like object with a long flowing tail – is a sight that graces our skies about once per decade, on average. These ‘great comets’ are surely among the most beautiful objects that we can see in the heavens, and it is no wonder that they created such fear in earlier times. Just what makes a comet ‘‘great’’ is not easy to define. It is neither just about brightness nor only a matter of size. Some comets can sport prodigiously long tails and yet not be regarded as great. Others can become very bright, but hardly anyone other than a handful of enthusiastic astronomers will ever see them. Much depends on their separation from the Sun, the intensity of the tail, and so forth.

Author: Takeyuki Hida
Publisher: Springer Science & Business Media
ISBN: 9401736804
Category : Mathematics
Languages : en
Pages : 528

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Many areas of applied mathematics call for an efficient calculus in infinite dimensions. This is most apparent in quantum physics and in all disciplines of science which describe natural phenomena by equations involving stochasticity. With this monograph we intend to provide a framework for analysis in infinite dimensions which is flexible enough to be applicable in many areas, and which on the other hand is intuitive and efficient. Whether or not we achieved our aim must be left to the judgment of the reader. This book treats the theory and applications of analysis and functional analysis in infinite dimensions based on white noise. By white noise we mean the generalized Gaussian process which is (informally) given by the time derivative of the Wiener process, i.e., by the velocity of Brownian mdtion. Therefore, in essence we present analysis on a Gaussian space, and applications to various areas of sClence. Calculus, analysis, and functional analysis in infinite dimensions (or dimension-free formulations of these parts of classical mathematics) have a long history. Early examples can be found in the works of Dirichlet, Euler, Hamilton, Lagrange, and Riemann on variational problems. At the beginning of this century, Frechet, Gateaux and Volterra made essential contributions to the calculus of functions over infinite dimensional spaces. The important and inspiring work of Wiener and Levy followed during the first half of this century. Moreover, the articles and books of Wiener and Levy had a view towards probability theory.

Author: Michiel Hazewinkel
Publisher: Springer Science & Business Media
ISBN: 9400959915
Category : Mathematics
Languages : en
Pages : 555

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This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author: M. Hazewinkel
Publisher: Springer
ISBN: 1489937935
Category : Mathematics
Languages : en
Pages : 952

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Author: Peter Schneider
Publisher: Springer Science & Business Media
ISBN: 3662047284
Category : Mathematics
Languages : en
Pages : 159

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This book grew out of a course which I gave during the winter term 1997/98 at the Universitat Munster. The course covered the material which here is presented in the first three chapters. The fourth more advanced chapter was added to give the reader a rather complete tour through all the important aspects of the theory of locally convex vector spaces over nonarchimedean fields. There is one serious restriction, though, which seemed inevitable to me in the interest of a clear presentation. In its deeper aspects the theory depends very much on the field being spherically complete or not. To give a drastic example, if the field is not spherically complete then there exist nonzero locally convex vector spaces which do not have a single nonzero continuous linear form. Although much progress has been made to overcome this problem a really nice and complete theory which to a large extent is analogous to classical functional analysis can only exist over spherically complete field8. I therefore allowed myself to restrict to this case whenever a conceptual clarity resulted. Although I hope that thi8 text will also be useful to the experts as a reference my own motivation for giving that course and writing this book was different. I had the reader in mind who wants to use locally convex vector spaces in the applications and needs a text to quickly gra8p this theory.

Author: Zhi-yuan Huang
Publisher: Springer Science & Business Media
ISBN: 9401141088
Category : Mathematics
Languages : en
Pages : 308

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The infinite dimensional analysis as a branch of mathematical sciences was formed in the late 19th and early 20th centuries. Motivated by problems in mathematical physics, the first steps in this field were taken by V. Volterra, R. GateallX, P. Levy and M. Frechet, among others (see the preface to Levy[2]). Nevertheless, the most fruitful direction in this field is the infinite dimensional integration theory initiated by N. Wiener and A. N. Kolmogorov which is closely related to the developments of the theory of stochastic processes. It was Wiener who constructed for the first time in 1923 a probability measure on the space of all continuous functions (i. e. the Wiener measure) which provided an ideal math ematical model for Brownian motion. Then some important properties of Wiener integrals, especially the quasi-invariance of Gaussian measures, were discovered by R. Cameron and W. Martin[l, 2, 3]. In 1931, Kolmogorov[l] deduced a second partial differential equation for transition probabilities of Markov processes order with continuous trajectories (i. e. diffusion processes) and thus revealed the deep connection between theories of differential equations and stochastic processes. The stochastic analysis created by K. Ito (also independently by Gihman [1]) in the forties is essentially an infinitesimal analysis for trajectories of stochastic processes. By virtue of Ito's stochastic differential equations one can construct diffusion processes via direct probabilistic methods and treat them as function als of Brownian paths (i. e. the Wiener functionals).

Author: I_Uri_ Makarovich Berezanski_
Publisher: American Mathematical Soc.
ISBN: 9780821898130
Category : Mathematics
Languages : en
Pages : 404

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Questions in the spectral theory of selfadjoint and normal operators acting in spaces of functions of infinitely many variables are studied in this book, and, in particular, the theory of expansions in generalized eigenfunctions of such operators. Both individual operators and arbitrary commuting families of them are considered. A theory of generalized functions of infinitely many variables is constructed. The circle of questions presented has evolved in recent years, especially in connection with problems in quantum field theory. This book will be useful to mathematicians and physicists interested in the indicated questions, as well as to graduate students and students in advanced university courses.

Author: Yau-Chuen Wong
Publisher: Routledge
ISBN: 1351436457
Category : Mathematics
Languages : en
Pages : 206

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This text offers an overview of the basic theories and techniques of functional analysis and its applications. It contains topics such as the fixed point theory starting from Ky Fan's KKM covering and quasi-Schwartz operators. It also includes over 200 exercises to reinforce important concepts.;The author explores three fundamental results on Banach spaces, together with Grothendieck's structure theorem for compact sets in Banach spaces (including new proofs for some standard theorems) and Helley's selection theorem. Vector topologies and vector bornologies are examined in parallel, and their internal and external relationships are studied. This volume also presents recent developments on compact and weakly compact operators and operator ideals; and discusses some applications to the important class of Schwartz spaces.;This text is designed for a two-term course on functional analysis for upper-level undergraduate and graduate students in mathematics, mathematical physics, economics and engineering. It may also be used as a self-study guide by researchers in these disciplines.

Author:
Publisher: Springer Science & Business Media
ISBN: 3322905594
Category : Technology & Engineering
Languages : en
Pages : 549

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The present book grew out of several courses which I have taught at the University of Zürich and at the University of Maryland during the past seven years. It is primarily intended to be a systematic text on locally convex spaces at the level of a student who has some familiarity with general topology and basic measure theory. However, since much of the material is of fairly recent origin and partly appears here for the first time in a book, and also since some well-known material has been given a not so well-known treatment, I hope that this book might prove useful even to more advanced readers. And in addition I hope that the selection ofmaterial marks a sufficient set-offfrom the treatments in e.g. N. Bourbaki [4], [5], R.E. Edwards [1], K. Floret-J. Wloka [1], H.G. Garnir-M. De Wilde-J. Schmets [1], AGrothendieck [13], H. Heuser [1], J. Horvath [1], J.L. Kelley-I. Namioka et al. [1], G. Köthe [7], [10], A P. Robertson W. Robertson [1], W. Rudin [2], H.H. Schaefer [1], F. Treves [l], A Wilansky [1]. A few sentences should be said about the organization of the book. It consists of 21 chapters which are grouped into three parts. Each chapter splits into several sections. Chapters, sections, and the statements therein are enumerated in consecutive fashion.