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Differential Calculus In Locally Convex Spaces
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Book Synopsis Differential Calculus in Locally Convex Spaces by : H.H. Keller
Download or read book Differential Calculus in Locally Convex Spaces written by H.H. Keller and published by Springer. This book was released on 2006-11-15 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential calculus in locally convex spaces by : Hans Heinrich Keller
Download or read book Differential calculus in locally convex spaces written by Hans Heinrich Keller and published by . This book was released on 1974 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Calculus and Holomorphy by : J.F. Colombeau
Download or read book Differential Calculus and Holomorphy written by J.F. Colombeau and published by Elsevier. This book was released on 2011-08-18 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential Calculus and Holomorphy
Book Synopsis Locally Convex Spaces and Linear Partial Differential Equations by : François Treves
Download or read book Locally Convex Spaces and Linear Partial Differential Equations written by François Treves and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is hardly an exaggeration to say that, if the study of general topolog ical vector spaces is justified at all, it is because of the needs of distribu tion and Linear PDE * theories (to which one may add the theory of convolution in spaces of hoi om orphic functions). The theorems based on TVS ** theory are generally of the "foundation" type: they will often be statements of equivalence between, say, the existence - or the approx imability -of solutions to an equation Pu = v, and certain more "formal" properties of the differential operator P, for example that P be elliptic or hyperboJic, together with properties of the manifold X on which P is defined. The latter are generally geometric or topological, e. g. that X be P-convex (Definition 20. 1). Also, naturally, suitable conditions will have to be imposed upon the data, the v's, and upon the stock of possible solutions u. The effect of such theorems is to subdivide the study of an equation like Pu = v into two quite different stages. In the first stage, we shall look for the relevant equivalences, and if none is already available in the literature, we shall try to establish them. The second stage will consist of checking if the "formal" or "geometric" conditions are satisfied.
Book Synopsis Differential Calculus for Locally Convex Topological Vector Spaces by : Mir Kursheed Ali
Download or read book Differential Calculus for Locally Convex Topological Vector Spaces written by Mir Kursheed Ali and published by . This book was released on 1965 with total page 32 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convex Analysis In General Vector Spaces by : C Zalinescu
Download or read book Convex Analysis In General Vector Spaces written by C Zalinescu and published by World Scientific. This book was released on 2002-07-30 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 subdifferential 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.
Book Synopsis A Theory of Differentiation in Locally Convex Spaces by : Sadayuki Yamamuro
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.
Book Synopsis Foundations of Complex Analysis in Non Locally Convex Spaces by : A. Bayoumi
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.
Book Synopsis Calculus in Vector Spaces without Norm by : A. Frölicher
Download or read book Calculus in Vector Spaces without Norm written by A. Frölicher and published by Springer. This book was released on 2006-11-15 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convex Analysis and Beyond by : Boris S. Mordukhovich
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.
Book Synopsis Locally Convex Spaces by : M. Scott Osborne
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.
Book Synopsis Differential Calculus and Holomorphy by : Jean François Colombeau
Download or read book Differential Calculus and Holomorphy written by Jean François Colombeau and published by . This book was released on 1982 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Calculus and Differentiable Partitions of Unity in Locally Convex Spaces by : Yee Pong Wong
Download or read book Differential Calculus and Differentiable Partitions of Unity in Locally Convex Spaces written by Yee Pong Wong and published by c1975.. This book was released on 1975 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Differential Calculus in Topological Linear Spaces by : Sadayuki Yamamuro
Download or read book Differential Calculus in Topological Linear Spaces written by Sadayuki Yamamuro and published by . This book was released on 1974 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Topological Vector Spaces and Their Applications by : V.I. Bogachev
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.
Book Synopsis Analytic Sets in Locally Convex Spaces by : P. Mazet
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
Book Synopsis Convex Analysis and Measurable Multifunctions by : C. Castaing
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.