Mathematical Analysis and Applications

Author: Michael Ruzhansky
Publisher: John Wiley & Sons
ISBN: 9781119414308
Release Date: 2018-04-05
Genre: Mathematics

An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields. Michael Ruzhansky, Ph.D., is Professor in the Department of Mathematics at Imperial College London, UK. Dr. Ruzhansky was awarded the Ferran Sunyer I Balaguer Prize in 2014. Hemen Dutta, Ph.D., is Senior Assistant Professor of Mathematics at Gauhati University, India. Ravi P. Agarwal, Ph.D., is Professor and Chair of the Department of Mathematics at Texas A&M University-Kingsville, Kingsville, USA.

Finite Blaschke Products and Their Connections

Author: Stephan Ramon Garcia
Publisher: Springer
ISBN: 9783319782478
Release Date: 2018-05-24
Genre: Mathematics

This monograph offers an introduction to finite Blaschke products and their connections to complex analysis, linear algebra, operator theory, matrix analysis, and other fields. Old favorites such as the Carathéodory approximation and the Pick interpolation theorems are featured, as are many topics that have never received a modern treatment, such as the Bohr radius and Ritt's theorem on decomposability. Deep connections to hyperbolic geometry are explored, as are the mapping properties, zeros, residues, and critical points of finite Blaschke products. In addition, model spaces, rational functions with real boundary values, spectral mapping properties of the numerical range, and the Darlington synthesis problem from electrical engineering are also covered. Topics are carefully discussed, and numerous examples and illustrations highlight crucial ideas. While thorough explanations allow the reader to appreciate the beauty of the subject, relevant exercises following each chapter improve technical fluency with the material. With much of the material previously scattered throughout mathematical history, this book presents a cohesive, comprehensive and modern exposition accessible to undergraduate students, graduate students, and researchers who have familiarity with complex analysis.

Hilbert Space Methods in Signal Processing

Author: Rodney A. Kennedy
Publisher: Cambridge University Press
ISBN: 9781107010031
Release Date: 2013-03-07
Genre: Mathematics

An accessible introduction to Hilbert spaces, combining the theory with applications of Hilbert methods in signal processing.

Digital Nets and Sequences

Author: Josef Dick
Publisher: Cambridge University Press
ISBN: 9781139490054
Release Date: 2010-09-09
Genre: Computers

Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi–Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte Carlo method, quasi–Monte Carlo rules have increased in popularity, with many fruitful applications in mathematical practice. These rules require nodes with good uniform distribution properties, and digital nets and sequences in the sense of Niederreiter are known to be excellent candidates. Besides the classical theory, the book contains chapters on reproducing kernel Hilbert spaces and weighted integration, duality theory for digital nets, polynomial lattice rules, the newest constructions by Niederreiter and Xing and many more. The authors present an accessible introduction to the subject based mainly on material taught in undergraduate courses with numerous examples, exercises and illustrations.

Hilbert

Author: Constance Reid
Publisher: Springer-Verlag
ISBN: 9783662286159
Release Date: 2013-07-02
Genre: Mathematics


Introduction to Model Spaces and their Operators

Author: Stephan Ramon Garcia
Publisher: Cambridge University Press
ISBN: 9781107108745
Release Date: 2016-05-06
Genre: Mathematics

A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.

Proceedings

Author:
Publisher:
ISBN: UCSC:32106018412426
Release Date: 2005
Genre: Artificial intelligence


Mathematisches Denken

Author: T.W. Körner
Publisher: Springer-Verlag
ISBN: 9783034850018
Release Date: 2013-08-13
Genre: Science

Dieses Buch wendet sich zuallererst an intelligente Schüler ab 14 Jahren sowie an Studienanfänger, die sich für Mathematik interessieren und etwas mehr als die Anfangsgründe dieser Wissenschaft kennenlernen möchten. Es gibt inzwischen mehrere Bücher, die eine ähnliche Zielstellung verfolgen. Besonders gern erinnere ich mich an das Werk Vom Einmaleins zum Integral von Colerus, das ich in meiner Kindheit las. Es beginnt mit der folgenden entschiedenen Feststellung: Die Mathematik ist eine Mausefalle. Wer einmal in dieser Falle gefangen sitzt, findet selten den Ausgang, der zurück in seinen vormathematischen Seelenzustand leitet. ([49], S. 7) Einige dieser Bücher sind im Anhang zusammengestellt und kommen tiert. Tatsächlich ist das Unternehmen aber so lohnenswert und die Anzahl der schon vorhandenen Bücher doch so begrenzt, daß ich mich nicht scheue, ihnen ein weiteres hinzuzufügen. An zahlreichen amerikanischen Universitäten gibt es Vorlesungen, die gemeinhin oder auch offiziell als ,,Mathematik für Schöngeister'' firmieren. Dieser Kategorie ist das vorliegende Buch nicht zuzuordnen. Statt dessen soll es sich um eine ,,Mathematik für Mathematiker'' handeln, für Mathema tiker freilich, die noch sehr wenig von der Mathematik verstehen. Weshalb aber sollte nicht der eine oder andere von ihnen eines Tages den Autor dieses 1 Buches durch seine Vorlesungen in Staunen versetzen? Ich hoffe, daß auch meine Mathematikerkollegen Freude an dem Werk haben werden, und ich würde mir wünschen, daß auch andere Leser, bei denen die Wertschätzung für die Mathematik stärker als die Furcht vor ihr ist, Gefallen an ihm finden mögen.

Integralgleichungen

Author:
Publisher: Springer-Verlag
ISBN: 9783663103721
Release Date: 2013-07-02
Genre: Technology & Engineering