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Real Function Algebras

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Real Function Algebras

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Author : S.H. Kulkarni
language : en
Publisher: CRC Press
Release Date : 2020-08-26

Real Function Algebras written by S.H. Kulkarni and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-08-26 with Mathematics categories.

This self-contained reference/text presents a thorough account of the theory of real function algebras. Employing the intrinsic approach, avoiding the complexification technique, and generalizing the theory of complex function algebras, this single-source volume includes: an introduction to real Banach algebras; various generalizations of the Stone-Weierstrass theorem; Gleason parts; Choquet and Shilov boundaries; isometries of real function algebras; extensive references; and a detailed bibliography.;Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the Bishop-Stone-Weierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f(2), Re f(3), and Re f(4); and the positivity of the real part of a linear functional on a subspace of C(X).;With over 600 display equations, this reference is for mathematical analysts; pure, applied, and industrial mathematicians; and theoretical physicists; and a text for courses in Banach algebras and function algebras.

Real Function Algebras

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Author : S.H. Kulkarni
language : en
Publisher: CRC Press
Release Date : 2020-08-27

Function Algebras On Finite Sets

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Author : Dietlinde Lau
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-23

Function Algebras On Finite Sets written by Dietlinde Lau and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-23 with Mathematics categories.

Functions which are defined on finite sets occur in almost all fields of mathematics. For more than 80 years algebras whose universes are such functions (so-called function algebras), have been intensively studied. This book gives a broad introduction to the theory of function algebras and leads to the cutting edge of research. To familiarize the reader from the very beginning on with the algebraic side of function algebras the more general concepts of the Universal Algebra is given in the first part of the book. The second part on fuction algebras covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, clone theory. This book is an insdispensible source on function algebras for graduate students and researchers in mathematical logic and theoretical computer science.

Complete Normed Algebras

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Author : Frank F. Bonsall
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Complete Normed Algebras written by Frank F. Bonsall and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The axioms of a complex Banach algebra were very happily chosen. They are simple enough to allow wide ranging fields of application, notably in harmonic analysis, operator theory and function algebras. At the same time they are tight enough to allow the development of a rich collection of results, mainly through the interplay of the elementary parts of the theories of analytic functions, rings, and Banach spaces. Many of the theorems are things of great beauty, simple in statement, surprising in content, and elegant in proof. We believe that some of them deserve to be known by every mathematician. The aim of this book is to give an account of the principal methods and results in the theory of Banach algebras, both commutative and non commutative. It has been necessary to apply certain exclusion principles in order to keep our task within bounds. Certain classes of concrete Banach algebras have a very rich literature, namely C*-algebras, function algebras, and group algebras. We have regarded these highly developed theories as falling outside our scope. We have not entirely avoided them, but have been concerned with their place in the general theory, and have stopped short of developing their special properties. For reasons of space and time we have omitted certain other topics which would quite naturally have been included, in particular the theories of multipliers and of extensions of Banach algebras, and the implications for Banach algebras of some of the standard algebraic conditions on rings.

Natural Function Algebras

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Author : Charles E. Rickart
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Natural Function Algebras written by Charles E. Rickart and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

The term "function algebra" usually refers to a uniformly closed algebra of complex valued continuous functions on a compact Hausdorff space. Such Banach alge bras, which are also called "uniform algebras", have been much studied during the past 15 or 20 years. Since the most important examples of uniform algebras consist of, or are built up from, analytic functions, it is not surprising that most of the work has been dominated by questions of analyticity in one form or another. In fact, the study of these special algebras and their generalizations accounts for the bulk of the re search on function algebras. We are concerned here, however, with another facet of the subject based on the observation that very general algebras of continuous func tions tend to exhibit certain properties that are strongly reminiscent of analyticity. Although there exist a variety of well-known properties of this kind that could be mentioned, in many ways the most striking is a local maximum modulus principle proved in 1960 by Hugo Rossi [RIl]. This result, one of the deepest and most elegant in the theory of function algebras, is an essential tool in the theory as we have developed it here. It holds for an arbitrary Banaeh algebra of £unctions defined on the spectrum (maximal ideal space) of the algebra. These are the algebras, along with appropriate generalizations to algebras defined on noncompact spaces, that we call "natural func tion algebras".

Glasnik Matematicki

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Author :
language : en
Publisher:
Release Date : 1997-06

Glasnik Matematicki written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06 with categories.

Canadian Journal Of Mathematics

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Author :
language : en
Publisher:
Release Date : 1981-02

Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981-02 with categories.

Clifford Algebra And Spinor Valued Functions

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Author : R. Delanghe
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Clifford Algebra And Spinor Valued Functions written by R. Delanghe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

This volume describes the substantial developments in Clifford analysis which have taken place during the last decade and, in particular, the role of the spin group in the study of null solutions of real and complexified Dirac and Laplace operators. The book has six main chapters. The first two (Chapters 0 and I) present classical results on real and complex Clifford algebras and show how lower-dimensional real Clifford algebras are well-suited for describing basic geometric notions in Euclidean space. Chapters II and III illustrate how Clifford analysis extends and refines the computational tools available in complex analysis in the plane or harmonic analysis in space. In Chapter IV the concept of monogenic differential forms is generalized to the case of spin-manifolds. Chapter V deals with analysis on homogeneous spaces, and shows how Clifford analysis may be connected with the Penrose transform. The volume concludes with some Appendices which present basic results relating to the algebraic and analytic structures discussed. These are made accessible for computational purposes by means of computer algebra programmes written in REDUCE and are contained on an accompanying floppy disk.

Canadian Journal Of Mathematics

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Author :
language : en
Publisher:
Release Date : 1988-10

Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-10 with categories.

Glasnik Matematicki

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Author :
language : en
Publisher:
Release Date : 1997-06

Glasnik Matematicki written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06 with categories.

Real Function Algebras

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