Ten Mathematical Essays On Approximation In Analysis And Topology

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Author: Juan Ferrera
Publisher: Elsevier
ISBN: 9780080459196
Size: 75.48 MB
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Ten Mathematical Essays On Approximation In Analysis And Topology by Juan Ferrera

Original Title: Ten Mathematical Essays On Approximation In Analysis And Topology

This book collects 10 mathematical essays on approximation in Analysis and Topology by some of the most influent mathematicians of the last third of the 20th Century. Besides the papers contain the very ultimate results in each of their respective fields, many of them also include a series of historical remarks about the state of mathematics at the time they found their most celebrated results, as well as some of their personal circumstances originating them, which makes particularly attractive the book for all scientist interested in these fields, from beginners to experts. These gem pieces of mathematical intra-history should delight to many forthcoming generations of mathematicians, who will enjoy some of the most fruitful mathematics of the last third of 20th century presented by their own authors. This book covers a wide range of new mathematical results. Among them, the most advanced characterisations of very weak versions of the classical maximum principle, the very last results on global bifurcation theory, algebraic multiplicities, general dependencies of solutions of boundary value problems with respect to variations of the underlying domains, the deepest available results in rapid monotone schemes applied to the resolution of non-linear boundary value problems, the intra-history of the the genesis of the first general global continuation results in the context of periodic solutions of nonlinear periodic systems, as well as the genesis of the coincidence degree, some novel applications of the topological degree for ascertaining the stability of the periodic solutions of some classical families of periodic second order equations, the resolution of a number of conjectures related to some very celebrated approximation problems in topology and inverse problems, as well as a number of applications to engineering, an extremely sharp discussion of the problem of approximating topological spaces by polyhedra using various techniques based on inverse systems, as well as homotopy expansions, and the Bishop-Phelps theorem. Key features: - It contains a number of seminal contributions by some of the most world leading mathematicians of the second half of the 20th Century. - The papers cover a complete range of topics, from the intra-history of the involved mathematics to the very last developments in Differential Equations, Inverse Problems, Analysis, Nonlinear Analysis and Topology. - All contributed papers are self-contained works containing rather complete list of references on each of the subjects covered. - The book contains some of the very last findings concerning the maximum principle, the theory of monotone schemes in nonlinear problems, the theory of algebraic multiplicities, global bifurcation theory, dynamics of periodic equations and systems, inverse problems and approximation in topology. - The papers are extremely well written and directed to a wide audience, from beginners to experts. An excellent occasion to become engaged with some of the most fruitful mathematics developed during the last decades.

Inverse Problems

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Author: Alexander G. Ramm
Publisher: Springer
ISBN: 9780387231952
Size: 46.72 MB
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Inverse Problems by Alexander G. Ramm

Original Title: Inverse Problems

Inverse Problems is a monograph which contains a self-contained presentation of the theory of several major inverse problems and the closely related results from the theory of ill-posed problems. The book is aimed at a large audience which include graduate students and researchers in mathematical, physical, and engineering sciences and in the area of numerical analysis.

Essays In Commutative Harmonic Analysis

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Author: C. C. Graham
Publisher: Springer Science & Business Media
ISBN: 1461299764
Size: 72.72 MB
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Essays In Commutative Harmonic Analysis by C. C. Graham

Original Title: Essays In Commutative Harmonic Analysis

This book considers various spaces and algebras made up of functions, measures, and other objects-situated always on one or another locally compact abelian group, and studied in the light of the Fourier transform. The emphasis is on the objects themselves, and on the structure-in-detail of the spaces and algebras. A mathematician needs to know only a little about Fourier analysis on the commutative groups, and then may go many ways within the large subject of harmonic analysis-into the beautiful theory of Lie group representations, for example. But this book represents the tendency to linger on the line, and the other abelian groups, and to keep asking questions about the structures thereupon. That tendency, pursued since the early days of analysis, has defined a field of study that can boast of some impressive results, and in which there still remain unanswered questions of compelling interest. We were influenced early in our careers by the mathematicians Jean-Pierre Kahane, Yitzhak Katznelson, Paul Malliavin, Yves Meyer, Joseph Taylor, and Nicholas Varopoulos. They are among the many who have made the field a productive meeting ground of probabilistic methods, number theory, diophantine approximation, and functional analysis. Since the academic year 1967-1968, when we were visitors in Paris and Orsay, the field has continued to see interesting developments. Let us name a few. Sam Drury and Nicholas Varopoulos solved the union problem for Helson sets, by proving a remarkable theorem (2.1.3) which has surely not seen its last use.

Generalized Inverses And Applications

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Author: M. Zuhair Nashed
Publisher: Elsevier
ISBN: 1483270297
Size: 31.93 MB
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Generalized Inverses And Applications by M. Zuhair Nashed

Original Title: Generalized Inverses And Applications

Generalized Inverses and Applications, contains the proceedings of an Advanced Seminar on Generalized Inverses and Applications held at the University of Wisconsin-Madison on October 8-10, 1973 under the auspices of the university's Mathematics Research Center. The seminar provided a forum for discussing the basic theory of generalized inverses and their applications to analysis and operator equations. Numerical analysis and approximation methods are considered, along with applications to statistics and econometrics, optimization, system theory, and operations research. Comprised of 14 chapters, this book begins by describing a unified approach to generalized inverses of linear operators, with particular reference to algebraic, topological, extremal, and proximinal properties. The reader is then introduced to the algebraic aspects of the generalized inverse of a rectangular matrix; the Fredholm pseudoinverse; and perturbations and approximations for generalized inverses and linear operator equations. Subsequent chapters deal with various applications of generalized inverses, including programming, games, and networks, as well as estimation and aggregation in econometrics. This monograph will be of interest to mathematicians and students of mathematics.


Download Read Online Mathematics  book
Author: Ida Kantor
Publisher: American Mathematical Soc.
ISBN: 1470422611
Size: 58.16 MB
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Mathematics by Ida Kantor

Original Title: Mathematics

Mathematics++ is a concise introduction to six selected areas of 20th century mathematics providing numerous modern mathematical tools used in contemporary research in computer science, engineering, and other fields. The areas are: measure theory, high-dimensional geometry, Fourier analysis, representations of groups, multivariate polynomials, and topology. For each of the areas, the authors introduce basic notions, examples, and results. The presentation is clear and accessible, stressing intuitive understanding, and it includes carefully selected exercises as an integral part. Theory is complemented by applications--some quite surprising--in theoretical computer science and discrete mathematics. The chapters are independent of one another and can be studied in any order. It is assumed that the reader has gone through the basic mathematics courses. Although the book was conceived while the authors were teaching Ph.D. students in theoretical computer science and discrete mathematics, it will be useful for a much wider audience, such as mathematicians specializing in other areas, mathematics students deciding what specialization to pursue, or experts in engineering or other fields.

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