Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is a short course on Banach space theory with special emphasis on certain aspects of the classical theory. In particular, the course focuses on three major topics: the elementary theory of Schauder bases, an introduction to Lp spaces, and an introduction to C(K) spaces. While these topics can be traced back to Banach himself, our primary interest is in the postwar renaissance of Banach space theory brought about by James, Lindenstrauss, Mazur, Namioka, Pelczynski, and others. Their elegant and insightful results are useful in many contemporary research endeavors and deserve greater publicity. By way of prerequisites, the reader will need an elementary understanding of functional analysis and at least a passing familiarity with abstract measure theory. An introductory course in topology would also be helpful; however, the text includes a brief appendix on the topology needed for the course.

Banach spaces. --- Banach, Espaces de --- Functions of complex variables --- Generalized spaces --- Topology

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Intended for a one year course, this volume serves as a single source, introducing students to the important techniques and theorems, while also containing enough background on advanced topics to appeal to those students wishing to specialize in Riemannian geometry. This is one of the few works to combine both the geometric parts of Riemannian geometry and the analytic aspects of the theory, while also presenting the most up-to-date research. This book will appeal to readers with a knowledge of standard manifold theory, including such topics as tensors and Stokes theorem. Various exercises are scattered throughout the text, helping motivate readers to deepen their understanding of the subject. Important additions to this new edition include: * A completely new coordinate free formula that is easily remembered, and is, in fact, the Koszul formula in disguise; * An increased number of coordinate calculations of connection and curvature; * General fomulas for curvature on Lie Groups and submersions; * Variational calculus has been integrated into the text, which allows for an early treatment of the Sphere theorem using a forgottten proof by Berger; * Several recent results about manifolds with positive curvature. From reviews of the first edition: "The book can be highly recommended to all mathematicians who want to get a more profound idea about the most interesting achievements in Riemannian geometry. It is one of the few comprehensive sources of this type." - Bernd Wegner, Zentralblatt.

Geometry, Differential. --- Geometry, Riemannian. --- Riemann geometry --- Riemannian geometry --- Generalized spaces --- Geometry, Non-Euclidean --- Semi-Riemannian geometry --- Differential geometry

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This is a graduate textbook covering an especially broad range of topics. The first part of the book contains a careful but rapid discussion of the basics of linear algebra, including vector spaces, linear transformations, quotient spaces, and isomorphism theorems. The author then proceeds to modules, emphasizing a comparison with vector spaces. A thorough discussion of inner product spaces, eigenvalues, eigenvectors, and finite dimensional spectral theory follows, culminating in the finite dimensional spectral theorem for normal operators. The second part of the book is a collection of topics, including metric vector spaces, metric spaces, Hilbert spaces, tensor products, and affine geometry. The last chapter discusses the umbral calculus, an area of modern algebra with many important applications. The new edition has been thoroughly rewritten, both in the text and exercise sets, and contains new chapters on convexity and separation, positive solutions to linear systems, singular values and QR decompostion. Treatments of tensor products and the umbral calculus have been greatly expanded and discussions of determinants, complexification of a real vector space, Schur's lemma and Gersgorin disks have been added. The author is Emeritus Professor of Mathematics, having taught at a number of universities, including MIT, UC Santa Barabara, the University of South Florida, the California State University at Fullerton and UC Irvine. He has written 27 books in mathematics at various levels and 9 books on computing. His interests lie mostly in the areas of algebra, set theory and logic, probability and finance.

Algebras, Linear. --- Linear algebra --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology --- Matrix theory. --- Linear and Multilinear Algebras, Matrix Theory. --- Algebra. --- Mathematics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Algebras, Linear --- Algèbre linéaire --- Linear algebra --- Algebras, Linear. --- Algebra, Universal --- Generalized spaces --- Mathematical analysis --- Calculus of operations --- Line geometry --- Topology

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book comes out of need and urgency (expressed especially in areas of Information Retrieval with respect to Image, Audio, Internet and Biology) to have a working tool to compare data.The book will provide powerful resource for all researchers using Mathematics as well as for mathematicians themselves. In the time when over-specialization and terminology fences isolate researchers, this Dictionary try to be ""centripedal"" and ""oikoumeni"", providing some access and altitude of vision but without taking the route of scientific vulgarisation. This attempted balance is the main ph

Metric spaces --- Distances --- Espaces métriques --- Measurement --- Mesure --- ELSEVIER-B EPUB-LIV-FT --- Metric spaces. --- Measurement. --- Spaces, Metric --- Generalized spaces --- Set theory --- Topology