Upper Bounds for Grothendieck Constants, Quantum Correlation Matrices and CCP Functions
Author: Frank Oertel
Publisher: Springer Nature
Published:
Total Pages: 238
ISBN-13: 3031572017
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Matrix Analysis and Entrywise Positivity Preservers
Author: Apoorva Khare
Publisher: Cambridge University Press
Published: 2022-03-31
Total Pages: 300
ISBN-13: 9781108792042
DOWNLOAD EBOOKMatrices and kernels with positivity structures, and the question of entrywise functions preserving them, have been studied throughout the 20th century, attracting recent interest in connection to high-dimensional covariance estimation. This is the first book to systematically develop the theoretical foundations of the entrywise calculus, focusing on entrywise operations - or transforms - of matrices and kernels with additional structure, which preserve positive semidefiniteness. Designed as an introduction for students, it presents an in-depth and comprehensive view of the subject, from early results to recent progress. Topics include: structural results about, and classifying the preservers of positive semidefiniteness and other Loewner properties (monotonicity, convexity, super-additivity); historical connections to metric geometry; classical connections to moment problems; and recent connections to combinatorics and Schur polynomials. Based on the author's course, the book is structured for use as lecture notes, including exercises for students, yet can also function as a comprehensive reference text for experts.
Upper and Lower Bounds for Stochastic Processes
Author: Michel Talagrand
Publisher: Springer Nature
Published: 2022-01-01
Total Pages: 727
ISBN-13: 3030825957
DOWNLOAD EBOOKThis book provides an in-depth account of modern methods used to bound the supremum of stochastic processes. Starting from first principles, it takes the reader to the frontier of current research. This second edition has been completely rewritten, offering substantial improvements to the exposition and simplified proofs, as well as new results. The book starts with a thorough account of the generic chaining, a remarkably simple and powerful method to bound a stochastic process that should belong to every probabilist’s toolkit. The effectiveness of the scheme is demonstrated by the characterization of sample boundedness of Gaussian processes. Much of the book is devoted to exploring the wealth of ideas and results generated by thirty years of efforts to extend this result to more general classes of processes, culminating in the recent solution of several key conjectures. A large part of this unique book is devoted to the author’s influential work. While many of the results presented are rather advanced, others bear on the very foundations of probability theory. In addition to providing an invaluable reference for researchers, the book should therefore also be of interest to a wide range of readers.
Tensor Norms and Operator Ideals
Author: A. Defant
Publisher: Elsevier
Published: 1992-11-26
Total Pages: 579
ISBN-13: 0080872875
DOWNLOAD EBOOKThe three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exercises.
Multidimensional Real Analysis I
Author: J. J. Duistermaat
Publisher: Cambridge University Press
Published: 2004-05-06
Total Pages: 444
ISBN-13: 1139451197
DOWNLOAD EBOOKPart one of the authors' comprehensive and innovative work on multidimensional real analysis. This book is based on extensive teaching experience at Utrecht University and gives a thorough account of differential analysis in multidimensional Euclidean space. It is an ideal preparation for students who wish to go on to more advanced study. The notation is carefully organized and all proofs are clean, complete and rigorous. The authors have taken care to pay proper attention to all aspects of the theory. In many respects this book presents an original treatment of the subject and it contains many results and exercises that cannot be found elsewhere. The numerous exercises illustrate a variety of applications in mathematics and physics. This combined with the exhaustive and transparent treatment of subject matter make the book ideal as either the text for a course, a source of problems for a seminar or for self study.
New QMaths 11A Teacher Resource Pack
Author: Natalie Dove
Publisher:
Published: 2002
Total Pages: 154
ISBN-13: 9780170104982
DOWNLOAD EBOOKThis resource pack has three components: - blackline masters that present supplementary exercises and answers on topics appropriate to Year 11 Mathematics A - a CD-ROM with PDFs of the blackline masters and a network licence for purchasers - another CD-ROM of the comlete New QMaths 11A student text, with a network licence for schools that have adopted the textbook.
