Author:
Publisher: Elsevier
ISBN: 0080871364
Category : Mathematics
Languages : en
Pages : 235
Book Description
This work deals with the many variations of the Stoneileierstrass Theorem for vector-valued functions and some of its applications. The book is largely self-contained. The amount of Functional Analysis required is minimal, except for Chapter 8. The book can be used by graduate students who have taken the usual first-year real and complex analysis courses.
Approximation of Vector Valued Functions
Author:
Publisher: Elsevier
ISBN: 0080871364
Category : Mathematics
Languages : en
Pages : 235
Book Description
This work deals with the many variations of the Stoneileierstrass Theorem for vector-valued functions and some of its applications. The book is largely self-contained. The amount of Functional Analysis required is minimal, except for Chapter 8. The book can be used by graduate students who have taken the usual first-year real and complex analysis courses.
Publisher: Elsevier
ISBN: 0080871364
Category : Mathematics
Languages : en
Pages : 235
Book Description
This work deals with the many variations of the Stoneileierstrass Theorem for vector-valued functions and some of its applications. The book is largely self-contained. The amount of Functional Analysis required is minimal, except for Chapter 8. The book can be used by graduate students who have taken the usual first-year real and complex analysis courses.
An Approximation Theorem for Vector-valued Functions
Author: M. Kisielewicz
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
Book Description
Publisher:
ISBN:
Category :
Languages : en
Pages : 16
Book Description
Approximation of Vector-valued Functions
Author: Lee W. Johnson
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 110
Book Description
Publisher:
ISBN:
Category : Functions
Languages : en
Pages : 110
Book Description
Approximation Properties of Vector Valued Functions
Author: Robert Creighton Buck
Publisher:
ISBN:
Category : Functional analysis
Languages : en
Pages : 15
Book Description
Set theory, Topology, TheoremsWeierstrass theorem, Modules(Mathematics)Let M be a closed C(X) submodule of the space C(X:E) of all bounded continuous functions on the compact space X with values in the normed linear space E. Then, it is shown that the linear functionals phi on C(X:E) that are extreme in the set of those which annihilate M and have norm at most one are exactly those of the form phi(g) = L(g(x sub 0)), where x sub 0 is a point of X and L is an extreme point of the set of functionals of norm one on E that annihilate the subspace M(x sub 0)=(all f(x sub 0) for f epsilon M). The proof uses various forms of the Weierstrass approximation theorem for modules. (Author).
Publisher:
ISBN:
Category : Functional analysis
Languages : en
Pages : 15
Book Description
Set theory, Topology, TheoremsWeierstrass theorem, Modules(Mathematics)Let M be a closed C(X) submodule of the space C(X:E) of all bounded continuous functions on the compact space X with values in the normed linear space E. Then, it is shown that the linear functionals phi on C(X:E) that are extreme in the set of those which annihilate M and have norm at most one are exactly those of the form phi(g) = L(g(x sub 0)), where x sub 0 is a point of X and L is an extreme point of the set of functionals of norm one on E that annihilate the subspace M(x sub 0)=(all f(x sub 0) for f epsilon M). The proof uses various forms of the Weierstrass approximation theorem for modules. (Author).
Vector-Valued Functions and their Applications
Author: Chuang-Gan Hu
Publisher: Springer Science & Business Media
ISBN: 9401580308
Category : Mathematics
Languages : en
Pages : 171
Book Description
This book is the first to be devoted to the theory of vector-valued functions with one variable. This theory is one of the fundamental tools employed in modern physics, the spectral theory of operators, approximation of analytic operators, analytic mappings between vectors, and vector-valued functions of several variables. The book contains three chapters devoted to the theory of normal functions, Hp-space, and vector-valued functions and their applications. Among the topics dealt with are the properties of complex functions in a complex plane and infinite-dimensional spaces, and the solution of vector-valued integral equations and boundary value problems by complex analysis and functional analysis, which involve methods which can be applied to problems in operations research and control theory. Much original research is included. This volume will be of interest to those whose work involves complex analysis and control theory, and can be recommended as a graduate text in these areas.
Publisher: Springer Science & Business Media
ISBN: 9401580308
Category : Mathematics
Languages : en
Pages : 171
Book Description
This book is the first to be devoted to the theory of vector-valued functions with one variable. This theory is one of the fundamental tools employed in modern physics, the spectral theory of operators, approximation of analytic operators, analytic mappings between vectors, and vector-valued functions of several variables. The book contains three chapters devoted to the theory of normal functions, Hp-space, and vector-valued functions and their applications. Among the topics dealt with are the properties of complex functions in a complex plane and infinite-dimensional spaces, and the solution of vector-valued integral equations and boundary value problems by complex analysis and functional analysis, which involve methods which can be applied to problems in operations research and control theory. Much original research is included. This volume will be of interest to those whose work involves complex analysis and control theory, and can be recommended as a graduate text in these areas.
Calculus of Vector Functions
Author: Richard E. Williamson
Publisher: Prentice Hall
ISBN:
Category : Mathematics
Languages : en
Pages : 644
Book Description
Publisher: Prentice Hall
ISBN:
Category : Mathematics
Languages : en
Pages : 644
Book Description
Approximation by Vector-valued Functions
Author: M. Brannigan
Publisher:
ISBN: 9780798811583
Category :
Languages : en
Pages : 10
Book Description
Publisher:
ISBN: 9780798811583
Category :
Languages : en
Pages : 10
Book Description
Approximation with Vector-valued Norms in Linear Spaces
Author: Alexander Constantine Bacopoulos
Publisher:
ISBN:
Category : Approximation
Languages : en
Pages : 146
Book Description
Publisher:
ISBN:
Category : Approximation
Languages : en
Pages : 146
Book Description
Rational Approximations from Power Series of Vector-valued Meromorphic Functions
Author: Avram Sidi
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 28
Book Description
Publisher:
ISBN:
Category : Approximation theory
Languages : en
Pages : 28
Book Description
Vector Calculus
Author: Miroslav Lovric
Publisher: John Wiley & Sons
ISBN: 0471725692
Category : Mathematics
Languages : en
Pages : 638
Book Description
This book gives a comprehensive and thorough introduction to ideas and major results of the theory of functions of several variables and of modern vector calculus in two and three dimensions. Clear and easy-to-follow writing style, carefully crafted examples, wide spectrum of applications and numerous illustrations, diagrams, and graphs invite students to use the textbook actively, helping them to both enforce their understanding of the material and to brush up on necessary technical and computational skills. Particular attention has been given to the material that some students find challenging, such as the chain rule, Implicit Function Theorem, parametrizations, or the Change of Variables Theorem.
Publisher: John Wiley & Sons
ISBN: 0471725692
Category : Mathematics
Languages : en
Pages : 638
Book Description
This book gives a comprehensive and thorough introduction to ideas and major results of the theory of functions of several variables and of modern vector calculus in two and three dimensions. Clear and easy-to-follow writing style, carefully crafted examples, wide spectrum of applications and numerous illustrations, diagrams, and graphs invite students to use the textbook actively, helping them to both enforce their understanding of the material and to brush up on necessary technical and computational skills. Particular attention has been given to the material that some students find challenging, such as the chain rule, Implicit Function Theorem, parametrizations, or the Change of Variables Theorem.