
Analysis and Probability
Wavelets, Signals, Fractals
Palle E. T. Jorgensen(Author)
Springer (Publisher)
Published on 19. September 2006
Book
Hardback
XLVIII, 280 pages
978-0-387-29519-0 (ISBN)
Description
If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is. -John von Neumann While this is a course in analysis, our approach departs from the beaten path in some ways. Firstly, we emphasize a variety of connections to themes from neighboring fields, such as wavelets, fractals and signals; topics typically not included in a gradu ate analysis course. This in turn entails excursions into domains with a probabilistic flavor. Yet the diverse parts of the book follow a common underlying thread, and to gether they constitute a good blend; each part in the mix naturally complements the other. In fact, there are now good reasons for taking a wider view of analysis, for ex ample the fact that several applied trends have come to interact in new and exciting ways with traditional mathematical analysis-as it was taught in graduate classes for generations. One consequence of these impulses from "outside" is that conventional boundaries between core disciplines in mathematics have become more blurred. Fortunately this branching out does not mean that students will need to start out with any different or additional prerequisites. In fact, the ideas involved in this book are intuitive, natural, many of them visual, and geometric. The required background is quite minimal and it does not go beyond what is typically required in most graduate programs.
Reviews / Votes
From the reviews: "I find that the best texts ... are those drawn from lectures delivered to varied audiences over time. This is such a book ... . it also goes further than many to clear a pathway to success for the diligent reader. ... discusses the content of the recommended works and their specific topical relation to each chapter in concluding sections entitled 'References and remarks'. The additional remarks make all the difference. That form of presentation is why this text has excellent motivation throughout ... ." (Tom Schulte, MathDL, February, 2007) "In this book, an entry in Springer's Graduate Texts in Mathematics series, the author has made the effort to put enough material on probability theory, wavelets and frames, operators, Cuntz algebras, and the Perron-Frobenius theorem ... The illustrations, including graphs of wavelets and signal processing diagrams, are plentiful and illuminating. The multitude of topics in mathematics covered and the links between them that are described in this book mean that there is something for everyone." (Judith A. Packer, Mathematical Reviews, Issue 2008 a)More details
Series
Edition
2006 ed.
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
XLVIII, 280 p.
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 23 mm
Weight
658 gr
ISBN-13
978-0-387-29519-0 (9780387295190)
DOI
10.1007/978-0-387-33082-2
Schweitzer Classification
Other editions
Additional editions

Book
11/2010
Springer
€53.49
Shipment within 15-20 days

E-Book
10/2007
1st Edition
Springer
€44.02
Available for download
Persons
Palle Jorgensen is a Professor of mathematics at the University of Iowa, Iowa City, USA; previously he taught at Stanford University, at Aarhus University (Denmark), and at the University of Pennsylvania. He is a research mathematician, funded over his career, in part, by the USA Natl. Sci. Foundation (NSF), and by bi-national research grants, most recently BSF (USA-Israel). He has had 27 PhD students. His research papers have appeared in international scientific journals - in mathematics, both pure and applied; including multiple areas: operator algebras, harmonic analysis, stochastic analysis, signal/image processing, and in mathematical physics (quantum theory). His recent research is focused on wavelet theory, dynamical systems, Gaussian processes, subdivision algorithms, spectral-tile duality, scaling and fractals. He has more than 280 published research papers, and is the author of eight books and research monographs.
Sergey Bezuglyi works at the University of Iowa since2016.He taught also in the Washington University, Ohio State University, and University of Oregon. Most of his research was conducted at the National Academy of Sciences of Ukraine when he was a Leading Researcher at the Institute for Low Temperature Physics in Kharkiv. His areas of interest in pure mathematics are ergodic theory, topological dynamics, operator algebras, functional analysis, and theory of operators.
His research was funded by national and international grants. Sergey Bezuglyi was awarded by the State Prize of Ukrainein 2010 for achievements in the theory of dynamical system.
Content
Introduction: Measures on path space.- Transition probabilities: Random walk.- ?o vs. ?.- A case study: Duality for Cantor sets.- Infinite products.- The minimal eigenfunction.- Generalizations and applications.- Pyramids and operators.- Pairs of representations of the Cuntz algebras , and their application to multiresolutions.