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Topological Vector Spaces Distributions and Kernels

Topological Vector Spaces  Distributions and Kernels Author Francois Treves
ISBN-10 9780486318103
Release 2013-09-03
Pages 592
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Extending beyond the boundaries of Hilbert and Banach space theory, this text focuses on key aspects of functional analysis, particularly in regard to solving partial differential equations. 1967 edition.



Topological Vector Spaces and Distributions

Topological Vector Spaces and Distributions Author John Horvath
ISBN-10 9780486311036
Release 2013-10-03
Pages 464
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"The most readable introduction to the theory of vector spaces available in English and possibly any other language."—J. L. B. Cooper, MathSciNet Review Mathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers. The precise exposition of the first three chapters—covering Banach spaces, locally convex spaces, and duality—provides an excellent summary of the modern theory of locally convex spaces. The fourth and final chapter develops the theory of distributions in relation to convolutions, tensor products, and Fourier transforms. Augmented with many examples and exercises, the text includes an extensive bibliography.



Basic Methods of Linear Functional Analysis

Basic Methods of Linear Functional Analysis Author John D. Pryce
ISBN-10 9780486173634
Release 2014-05-05
Pages 320
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Introduction to the themes of mathematical analysis, geared toward advanced undergraduate and graduate students. Topics include operators, function spaces, Hilbert spaces, and elementary Fourier analysis. Numerous exercises and worked examples.1973 edition.



Topological Vector Spaces and Their Applications

Topological Vector Spaces and Their Applications Author Vladimir I. Bogachev
ISBN-10 9783319571171
Release 2017-05-30
Pages 456
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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.



Finite Dimensional Vector Spaces

Finite Dimensional Vector Spaces Author Paul R. Halmos
ISBN-10 9780486822266
Release 2017-05-24
Pages 208
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Classic, widely cited, and accessible treatment offers an ideal supplement to many traditional linear algebra texts. "Extremely well-written and logical, with short and elegant proofs." — MAA Reviews. 1958 edition.



Differential Geometry

Differential Geometry Author Heinrich W. Guggenheimer
ISBN-10 9780486157207
Release 2012-04-27
Pages 400
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This text contains an elementary introduction to continuous groups and differential invariants; an extensive treatment of groups of motions in euclidean, affine, and riemannian geometry; more. Includes exercises and 62 figures.



Topological Spaces

Topological Spaces Author Claude Berge
ISBN-10 0486696537
Release 1963
Pages 270
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Excellent study of sets in topological spaces and topological vector spaces includes systematic development of the properties of multi-valued functions. Topics include families of sets, topological spaces, mappings of one set into another, ordered sets, more. Examples included from different domains. 1963 edition.



The Geometry of Heisenberg Groups

The Geometry of Heisenberg Groups Author Ernst Binz
ISBN-10 9780821844953
Release 2008
Pages 299
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The three-dimensional Heisenberg group, being the simplest non-commutative Lie group, appears prominently in various applications of mathematics. The goal of this book is to present basic geometric and algebraic properties of the Heisenberg group and its relation to other important mathematical structures (the skew field of quaternions, symplectic structures, and representations) and to describe some of its applications. In particular, the authors address such subjects as well as signal analysis and processing, geometric optics, and quantization. In each case, the authors present necessary details of the applied topic being considered. With no prerequisites beyond the standard mathematical curriculum, this book manages to encompass a large variety of topics being easily accessible in its fundamentals. It can be useful to students and researchers working in mathematics and in applied mathematics.



An Introduction to the Theory of Reproducing Kernel Hilbert Spaces

An Introduction to the Theory of Reproducing Kernel Hilbert Spaces Author Vern I. Paulsen
ISBN-10 9781316558737
Release 2016-04-11
Pages
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Reproducing kernel Hilbert spaces have developed into an important tool in many areas, especially statistics and machine learning, and they play a valuable role in complex analysis, probability, group representation theory, and the theory of integral operators. This unique text offers a unified overview of the topic, providing detailed examples of applications, as well as covering the fundamental underlying theory, including chapters on interpolation and approximation, Cholesky and Schur operations on kernels, and vector-valued spaces. Self-contained and accessibly written, with exercises at the end of each chapter, this unrivalled treatment of the topic serves as an ideal introduction for graduate students across mathematics, computer science, and engineering, as well as a useful reference for researchers working in functional analysis or its applications.



A Combinatorial Introduction to Topology

A Combinatorial Introduction to Topology Author Michael Henle
ISBN-10 0486679667
Release 1979
Pages 310
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Excellent text covers vector fields, plane homology and the Jordan Curve Theorem, surfaces, homology of complexes, more. Problems and exercises. Some knowledge of differential equations and multivariate calculus required.Bibliography. 1979 edition.



An Advanced Complex Analysis Problem Book

An Advanced Complex Analysis Problem Book Author Daniel Alpay
ISBN-10 9783319160597
Release 2015-11-13
Pages 521
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This is an exercises book at the beginning graduate level, whose aim is to illustrate some of the connections between functional analysis and the theory of functions of one variable. A key role is played by the notions of positive definite kernel and of reproducing kernel Hilbert space. A number of facts from functional analysis and topological vector spaces are surveyed. Then, various Hilbert spaces of analytic functions are studied.



Harmonic Analysis and the Theory of Probability

Harmonic Analysis and the Theory of Probability Author Salomon Bochner
ISBN-10 9780486154800
Release 2013-11-07
Pages 192
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Written by a distinguished mathematician and educator, this classic text emphasizes stochastic processes and the interchange of stimuli between probability and analysis. It also introduces the author's innovative concept of the characteristic functional. 1955 edition.



All the Mathematics You Missed

All the Mathematics You Missed Author
ISBN-10 7302090858
Release 2002
Pages 347
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All the Mathematics You Missed has been writing in one form or another for most of life. You can find so many inspiration from All the Mathematics You Missed also informative, and entertaining. Click DOWNLOAD or Read Online button to get full All the Mathematics You Missed book for free.



Uniform Distribution of Sequences

Uniform Distribution of Sequences Author L. Kuipers
ISBN-10 9780486149998
Release 2012-05-24
Pages 416
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The theory of uniform distribution began with Weyl's celebrated paper of 1916 and this book summarizes its development through the mid-1970s, with comprehensive coverage of methods and principles. 1974 edition.



Function Theory of Several Complex Variables

Function Theory of Several Complex Variables Author Steven George Krantz
ISBN-10 9780821827246
Release 2001
Pages 564
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The theory of several complex variables can be studied from several different perspectives. In this book, Steven Krantz approaches the subject from the point of view of a classical analyst, emphasizing its function-theoretic aspects. He has taken particular care to write the book with the student in mind, with uniformly extensive and helpful explanations, numerous examples, and plentiful exercises of varying difficulty. In the spirit of a student-oriented text, Krantz begins with an introduction to the subject, including an insightful comparison of analysis of several complex variables with the more familiar theory of one complex variable. The main topics in the book include integral formulas, convexity and pseudoconvexity, methods from harmonic analysis, and several aspects of the $\overline{\partial}$ problem. Some further topics are zero sets of holomorphic functions, estimates, partial differential equations, approximation theory, the boundary behavior of holomorphic functions, inner functions, invariant metrics, and holomorphic mappings. While due attention is paid to algebraic aspects of several complex variables (sheaves, Cousin problems, etc.), the student with a background in real and complex variable theory, harmonic analysis, and differential equations will be most comfortable with this treatment. This book is suitable for a first graduate course in several complex variables.



Differentiable Measures and the Malliavin Calculus

Differentiable Measures and the Malliavin Calculus Author Vladimir Igorevich Bogachev
ISBN-10 9780821849934
Release 2010-07-21
Pages 488
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This book provides the reader with the principal concepts and results related to differential properties of measures on infinite dimensional spaces. In the finite dimensional case such properties are described in terms of densities of measures with respect to Lebesgue measure. In the infinite dimensional case new phenomena arise. For the first time a detailed account is given of the theory of differentiable measures, initiated by S. V. Fomin in the 1960s; since then the method has found many various important applications. Differentiable properties are described for diverse concrete classes of measures arising in applications, for example, Gaussian, convex, stable, Gibbsian, and for distributions of random processes. Sobolev classes for measures on finite and infinite dimensional spaces are discussed in detail. Finally, we present the main ideas and results of the Malliavin calculus--a powerful method to study smoothness properties of the distributions of nonlinear functionals on infinite dimensional spaces with measures. The target readership includes mathematicians and physicists whose research is related to measures on infinite dimensional spaces, distributions of random processes, and differential equations in infinite dimensional spaces. The book includes an extensive bibliography on the subject.



Circuits Matrices and Linear Vector Spaces

Circuits  Matrices and Linear Vector Spaces Author Lawrence P. Huelsman
ISBN-10 9780486280448
Release 2013-08-16
Pages 304
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This high-level text explains the mathematics behind basic circuit theory. It covers matrix algebra, the basic theory of n-dimensional spaces, and applications to linear systems. Numerous problems. 1963 edition.