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Author: S.H. Kulkarni Publisher: CRC Press ISBN: 100014884X Category : Mathematics Languages : en Pages : 204
Book Description
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.
Author: S.H. Kulkarni Publisher: CRC Press ISBN: 100014884X Category : Mathematics Languages : en Pages : 204
Book Description
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.
Author: S.H. Kulkarni Publisher: CRC Press ISBN: 1000105636 Category : Mathematics Languages : en Pages : 201
Book Description
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.
Author: Dietlinde Lau Publisher: Springer Science & Business Media ISBN: 3540360239 Category : Mathematics Languages : en Pages : 668
Book Description
Function Algebras on Finite Sets gives a broad introduction to the subject, leading up to the cutting edge of research. The general concepts of the Universal Algebra are given in the first part of the book, to familiarize the reader from the very beginning on with the algebraic side of function algebras. The second part covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, and clone theory.
Author: John Derbyshire Publisher: National Academies Press ISBN: 030909657X Category : Science Languages : en Pages : 391
Book Description
Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages-and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics-it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging.
Author: T.V. Tonev Publisher: Elsevier ISBN: 9780080872834 Category : Mathematics Languages : en Pages : 293
Book Description
Treated in this volume are selected topics in analytic &Ggr;-almost-periodic functions and their representations as &Ggr;-analytic functions in the big-plane; n-tuple Shilov boundaries of function spaces, minimal norm principle for vector-valued functions and their applications in the study of vector-valued functions and n-tuple polynomial and rational hulls. Applications to the problem of existence of n-dimensional complex analytic structures, analytic &Ggr;-almost-periodic structures and structures of &Ggr;-analytic big-manifolds respectively in commutative Banach algebra spectra are also discussed.
Author: Charles E. Rickart Publisher: Springer Science & Business Media ISBN: 1461380707 Category : Mathematics Languages : en Pages : 252
Book Description
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".
Author: Halsey Royden Publisher: Pearson Modern Classics for Advanced Mathematics Series ISBN: 9780134689494 Category : Functional analysis Languages : en Pages : 0
Book Description
This text is designed for graduate-level courses in real analysis. Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis.
Author: R. Delanghe Publisher: Springer Science & Business Media ISBN: 9401129223 Category : Mathematics Languages : en Pages : 501
Book Description
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.
Author: S.H. Kulkarni
Author: S.H. Kulkarni
Author: S.H. Kulkarni
Author: Dietlinde Lau
Author: Andrew Browder
Author: John Derbyshire
Author: T.V. Tonev
Author: Charles E. Rickart
Author: Halsey Royden
Author: Ion Suciu
Author: R. Delanghe