Author: S. DineenPublisher: Elsevier
ISBN: 9780080871684
Category : Mathematics
Languages : en
Pages : 491
Book Description
Complex Analysis in Locally Convex Spaces
Complex Analysis in Locally Convex Spaces
Author: S. DineenPublisher: Elsevier
ISBN: 9780080871684
Category : Mathematics
Languages : en
Pages : 491
Book Description
Complex Analysis in Locally Convex Spaces
Foundations of Complex Analysis in Non Locally Convex Spaces
Author: A. BayoumiPublisher: Elsevier
ISBN: 008053192X
Category : Mathematics
Languages : en
Pages : 304
Book Description
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.
Locally Convex Spaces
Author: M. Scott OsbornePublisher: Springer Science & Business Media
ISBN: 3319020455
Category : Mathematics
Languages : en
Pages : 213
Book Description
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.
Differential Calculus and Holomorphy
Author: J.F. ColombeauPublisher: Elsevier
ISBN: 9780080871752
Category : Mathematics
Languages : en
Pages : 454
Book Description
Differential Calculus and Holomorphy
Locally Convex Spaces over Non-Archimedean Valued Fields
Author: C. Perez-GarciaPublisher: Cambridge University Press
ISBN: 9780521192439
Category : Mathematics
Languages : en
Pages : 486
Book Description
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.
Complex Analysis on Infinite Dimensional Spaces
Author: Sean DineenPublisher: Springer Science & Business Media
ISBN: 1447108698
Category : Mathematics
Languages : en
Pages : 553
Book Description
Infinite dimensional holomorphy is the study of holomorphic or analytic func tions over complex topological vector spaces. The terms in this description are easily stated and explained and allow the subject to project itself ini tially, and innocently, as a compact theory with well defined boundaries. However, a comprehensive study would include delving into, and interacting with, not only the obvious topics of topology, several complex variables theory and functional analysis but also, differential geometry, Jordan algebras, Lie groups, operator theory, logic, differential equations and fixed point theory. This diversity leads to a dynamic synthesis of ideas and to an appreciation of a remarkable feature of mathematics - its unity. Unity requires synthesis while synthesis leads to unity. It is necessary to stand back every so often, to take an overall look at one's subject and ask "How has it developed over the last ten, twenty, fifty years? Where is it going? What am I doing?" I was asking these questions during the spring of 1993 as I prepared a short course to be given at Universidade Federal do Rio de Janeiro during the following July. The abundance of suit able material made the selection of topics difficult. For some time I hesitated between two very different aspects of infinite dimensional holomorphy, the geometric-algebraic theory associated with bounded symmetric domains and Jordan triple systems and the topological theory which forms the subject of the present book.
Analytic Sets in Locally Convex Spaces
Author: P. MazetPublisher: Elsevier
ISBN: 9780080872001
Category : Mathematics
Languages : en
Pages : 274
Book Description
Analytic Sets in Locally Convex Spaces
Locally Convex Spaces and Harmonic Analysis
Author: Philippe G. CiarletConvex Analysis and Measurable Multifunctions
Author: C. CastaingPublisher: Springer
ISBN: 3540373845
Category : Mathematics
Languages : en
Pages : 283
Book Description
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.
Finite or Infinite Dimensional Complex Analysis
Author: Joji KajiwaraPublisher: CRC Press
ISBN: 0429530005
Category : Mathematics
Languages : en
Pages : 674
Book Description
This volume presents the proceedings of the Seventh International Colloquium on Finite or Infinite Dimensional Complex Analysis held in Fukuoka, Japan. The contributions offer multiple perspectives and numerous research examples on complex variables, Clifford algebra variables, hyperfunctions and numerical analysis.