Palle E. T. Jorgensen

Analysis and Probability (eBook, PDF)

Wavelets, Signals, Fractals

• Format: PDF

Produktbeschreibung

Combines analysis and tools from probability, harmonic analysis, operator theory, and engineering (signal/image processing)

Interdisciplinary focus with hands-on approach, generous motivation and new pedagogical techniques

Numerous exercises reinforce fundamental concepts and hone computational skills

Separate sections explain engineering terms to mathematicians and operator theory to engineers

Examines modern trends

Fills a gap in the literature

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Produktdetails

• Verlag: Springer US
• Seitenzahl: 280
• Erscheinungstermin: 17. Oktober 2007
• Englisch
• ISBN-13: 9780387330822
• Artikelnr.: 43728105

Autorenporträt

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.

Inhaltsangabe

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.

Rezensionen

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)