Download or read book Analytic Sets in Locally Convex Spaces written by P. Mazet and published by Elsevier. This book was released on 2000-04-01 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic Sets in Locally Convex Spaces

Download or read book Complex Analysis in Locally Convex Spaces written by S. Dineen and published by Elsevier. This book was released on 2011-08-18 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complex Analysis in Locally Convex Spaces

Download or read book Barrelled Locally Convex Spaces written by P. Pérez Carreras and published by Elsevier. This book was released on 1987-03-01 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a systematic treatment of barrelled spaces, and of structures in which barrelledness conditions are significant. It is a fairly self-contained study of the structural theory of those spaces, concentrating on the basic phenomena in the theory, and presenting a variety of functional-analytic techniques.Beginning with some basic and important results in different branches of Analysis, the volume deals with Baire spaces, presents a variety of techniques, and gives the necessary definitions, exploring conditions on discs to ensure that they are absorbed by the barrels of the space. The abstract theory of barrelled spaces is then presented, as well as local completeness and its applications to the inheritance of the Mackey topology to subspaces. Further discussed is the abstract study of bornological and ultrabornological spaces; B- and Br-completeness; inductive limits; strong barrelledness conditions; characterizations of barrelled, bornological and (DF)-spaces in the context of spaces of type C(X); the stability of barrelledness conditions of topological tensor products and the related questions of commutability of inductive limits and tensor products; and the holomorphically significant properties of locally convex spaces as developed by Nachbin and others.

Download or read book Locally Convex Spaces written by M. Scott Osborne and published by Springer Science & Business Media. This book was released on 2013-11-08 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: For most practicing analysts who use functional analysis, the restriction to Banach spaces seen in most real analysis graduate texts is not enough for their research. This graduate text, while focusing on locally convex topological vector spaces, is intended to cover most of the general theory needed for application to other areas of analysis. Normed vector spaces, Banach spaces, and Hilbert spaces are all examples of classes of locally convex spaces, which is why this is an important topic in functional analysis. While this graduate text focuses on what is needed for applications, it also shows the beauty of the subject and motivates the reader with exercises of varying difficulty. Key topics covered include point set topology, topological vector spaces, the Hahn–Banach theorem, seminorms and Fréchet spaces, uniform boundedness, and dual spaces. The prerequisite for this text is the Banach space theory typically taught in a beginning graduate real analysis course.

Download or read book Foundations of Complex Analysis in Non Locally Convex Spaces written by A. Bayoumi and published by Elsevier. This book was released on 2003-11-11 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: All the existing books in Infinite Dimensional Complex Analysis focus on the problems of locally convex spaces. However, the theory without convexity condition is covered for the first time in this book. This shows that we are really working with a new, important and interesting field. Theory of functions and nonlinear analysis problems are widespread in the mathematical modeling of real world systems in a very broad range of applications. During the past three decades many new results from the author have helped to solve multiextreme problems arising from important situations, non-convex and non linear cases, in function theory. Foundations of Complex Analysis in Non Locally Convex Spaces is a comprehensive book that covers the fundamental theorems in Complex and Functional Analysis and presents much new material. The book includes generalized new forms of: Hahn-Banach Theorem, Multilinear maps, theory of polynomials, Fixed Point Theorems, p-extreme points and applications in Operations Research, Krein-Milman Theorem, Quasi-differential Calculus, Lagrange Mean-Value Theorems, Taylor series, Quasi-holomorphic and Quasi-analytic maps, Quasi-Analytic continuations, Fundamental Theorem of Calculus, Bolzano's Theorem, Mean-Value Theorem for Definite Integral, Bounding and weakly-bounding (limited) sets, Holomorphic Completions, and Levi problem. Each chapter contains illustrative examples to help the student and researcher to enhance his knowledge of theory of functions. The new concept of Quasi-differentiability introduced by the author represents the backbone of the theory of Holomorphy for non-locally convex spaces. In fact it is different but much stronger than the Frechet one. The book is intended not only for Post-Graduate (M.Sc.& Ph.D.) students and researchers in Complex and Functional Analysis, but for all Scientists in various disciplines whom need nonlinear or non-convex analysis and holomorphy methods without convexity conditions to model and solve problems. bull; The book contains new generalized versions of: i) Fundamental Theorem of Calculus, Lagrange Mean-Value Theorem in real and complex cases, Hahn-Banach Theorems, Bolzano Theorem, Krein-Milman Theorem, Mean value Theorem for Definite Integral, and many others. ii) Fixed Point Theorems of Bruower, Schauder and Kakutani's. bull; The book contains some applications in Operations research and non convex analysis as a consequence of the new concept p-Extreme points given by the author. bull; The book contains a complete theory for Taylor Series representations of the different types of holomorphic maps in F-spaces without convexity conditions. bull; The book contains a general new concept of differentiability stronger than the Frechet one. This implies a new Differentiable Calculus called Quasi-differential (or Bayoumi differential) Calculus. It is due to the author's discovery in 1995. bull; The book contains the theory of polynomials and Banach Stienhaus theorem in non convex spaces.

Download or read book Convex Analysis in General Vector Spaces written by C. Zalinescu and published by World Scientific. This book was released on 2002 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The primary aim of this book is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions.

Download or read book A Theory of Differentiation in Locally Convex Spaces written by Sadayuki Yamamuro and published by American Mathematical Soc.. This book was released on 1979 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt: A theory of differentiation is constructed on locally convex spaces based on the correspondence between the sets of semi-norms which induce original topologies.

Download or read book Locally Convex Spaces over Non Archimedean Valued Fields written by C. Perez-Garcia and published by Cambridge University Press. This book was released on 2010-01-07 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt: Non-Archimedean functional analysis, where alternative but equally valid number systems such as p-adic numbers are fundamental, is a fast-growing discipline widely used not just within pure mathematics, but also applied in other sciences, including physics, biology and chemistry. This book is the first to provide a comprehensive treatment of non-Archimedean locally convex spaces. The authors provide a clear exposition of the basic theory, together with complete proofs and new results from the latest research. A guide to the many illustrative examples provided, end-of-chapter notes and glossary of terms all make this book easily accessible to beginners at the graduate level, as well as specialists from a variety of disciplines.

Download or read book The Theory of Analytic Spaces written by Jørgen Hoffmann-Jørgensen and published by . This book was released on 1970 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Convex Analysis and Measurable Multifunctions written by C. Castaing and published by Springer. This book was released on 2006-11-15 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present work is devoted to convex analysis, measurable multifunctions and some of their applications. The only necessary prerequisite for an intelligent reading is a good knowledge of analysis (Bourbaki or Dunford-Schwartz are appropriate references.

Download or read book Various Publications Series written by Aarhus universitet. Matematisk institut and published by . This book was released on 1970 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Topological Vector Spaces I written by Gottfried Köthe and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is the author's aim to give a systematic account of the most im portant ideas, methods and results of the theory of topological vector spaces. After a rapid development during the last 15 years, this theory has now achieved a form which makes such an account seem both possible and desirable. This present first volume begins with the fundamental ideas of general topology. These are of crucial importance for the theory that follows, and so it seems necessary to give a concise account, giving complete proofs. This also has the advantage that the only preliminary knowledge required for reading this book is of classical analysis and set theory. In the second chapter, infinite dimensional linear algebra is considered in comparative detail. As a result, the concept of dual pair and linear topologies on vector spaces over arbitrary fields are intro duced in a natural way. It appears to the author to be of interest to follow the theory of these linearly topologised spaces quite far, since this theory can be developed in a way which closely resembles the theory of locally convex spaces. It should however be stressed that this part of chapter two is not needed for the comprehension of the later chapters. Chapter three is concerned with real and complex topological vector spaces. The classical results of Banach's theory are given here, as are fundamental results about convex sets in infinite dimensional spaces.

Download or read book Local Analytic Geometry written by Shreeram Shankar Abhyankar and published by World Scientific. This book was released on 2001 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides, for use in a graduate course or for self-study by graduate students, a well-motivated treatment of several topics, especially the following: (1) algebraic treatment of several complex variables; (2) geometric approach to algebraic geometry via analytic sets; (3) survey of local algebra; (4) survey of sheaf theory. The book has been written in the spirit of Weierstrass. Power series play the dominant role. The treatment, being algebraic, is not restricted to complex numbers, but remains valid over any complete-valued field. This makes it applicable to situations arising from number theory. When it is specialized to the complex case, connectivity and other topological properties come to the fore. In particular, via singularities of analytic sets, topological fundamental groups can be studied. In the transition from punctual to local, i.e. from properties at a point to properties near a point, the classical work of Osgood plays an important role. This gives rise to normic forms and the concept of the Osgoodian. Following Serre, the passage from local to global properties of analytic spaces is facilitated by introducing sheaf theory. Here the fundamental results are the coherence theorems of Oka and Cartan. They are followed by theory normalization due to Oka and Zariski in the analytic and algebraic cases, respectively. Contents: Elementary Theory in Cn; Weierstrass Preparation Theorem; Review from Local Algebra; Parameters in Power Series Rings; Analytic Sets; Language of Sheaves; Analytic Spaces. Readership: Graduate students and researchers in pure mathematics.

Download or read book Topological Vector Spaces and Their Applications written by V.I. Bogachev and published by Springer. This book was released on 2017-05-16 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a compact exposition of the fundamentals of the theory of locally convex topological vector spaces. Furthermore it contains a survey of the most important results of a more subtle nature, which cannot be regarded as basic, but knowledge which is useful for understanding applications. Finally, the book explores some of such applications connected with differential calculus and measure theory in infinite-dimensional spaces. These applications are a central aspect of the book, which is why it is different from the wide range of existing texts on topological vector spaces. Overall, this book develops differential and integral calculus on infinite-dimensional locally convex spaces by using methods and techniques of the theory of locally convex spaces. The target readership includes mathematicians and physicists whose research is related to infinite-dimensional analysis.

Download or read book Convex Analysis and Beyond written by Boris S. Mordukhovich and published by Springer Nature. This book was released on 2022-04-24 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a unified theory of convex functions, sets, and set-valued mappings in topological vector spaces with its specifications to locally convex, Banach and finite-dimensional settings. These developments and expositions are based on the powerful geometric approach of variational analysis, which resides on set extremality with its characterizations and specifications in the presence of convexity. Using this approach, the text consolidates the device of fundamental facts of generalized differential calculus to obtain novel results for convex sets, functions, and set-valued mappings in finite and infinite dimensions. It also explores topics beyond convexity using the fundamental machinery of convex analysis to develop nonconvex generalized differentiation and its applications. The text utilizes an adaptable framework designed with researchers as well as multiple levels of students in mind. It includes many exercises and figures suited to graduate classes in mathematical sciences that are also accessible to advanced students in economics, engineering, and other applications. In addition, it includes chapters on convex analysis and optimization in finite-dimensional spaces that will be useful to upper undergraduate students, whereas the work as a whole provides an ample resource to mathematicians and applied scientists, particularly experts in convex and variational analysis, optimization, and their applications.

Download or read book Locally Convex Spaces and Harmonic Analysis An Introduction written by Philippe G. Ciarlet and published by SIAM. This book was released on 2021-08-10 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained textbook covers the fundamentals of two basic topics of linear functional analysis: locally convex spaces and harmonic analysis. Readers will find detailed introductions to topological vector spaces, distribution theory, weak topologies, the Fourier transform, the Hilbert transform, and Calderón–Zygmund singular integrals. An ideal introduction to more advanced texts, the book complements Ciarlet’s Linear and Nonlinear Functional Analysis with Applications (SIAM), in which these two topics were not treated. Pedagogical features such as detailed proofs and 93 problems make the book ideal for a one-semester first-year graduate course or for self-study. The book is intended for advanced undergraduates and first-year graduate students and researchers. It is appropriate for courses on functional analysis, distribution theory, Fourier transform, and harmonic analysis.

Download or read book Derived Functors in Functional Analysis written by Jochen Wengenroth and published by Springer. This book was released on 2003-01-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: The text contains for the first time in book form the state of the art of homological methods in functional analysis like characterizations of the vanishing of the derived projective limit functor or the functors Ext1 (E, F) for Fréchet and more general spaces. The researcher in real and complex analysis finds powerful tools to solve surjectivity problems e.g. on spaces of distributions or to characterize the existence of solution operators. The requirements from homological algebra are minimized: all one needs is summarized on a few pages. The answers to several questions of V.P. Palamodov who invented homological methods in analysis also show the limits of the program.