Analysis and Probability: Wavelets, Signals, Fractals (Graduate Texts in Mathematics, Band 234) - Softcover

Jorgensen, Palle E. T.

Softcover

ISBN 10: 1441921265 ISBN 13: 9781441921260

Verlag: Springer, 2010

Inhaltsangabe

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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Über die Autorin bzw. den Autor

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.

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This book, combining analysis and tools from mathematical probability, focuses on a systematic and novel presentation of recent trends in pure and applied mathematics: the emergence of three fields, wavelets, signals and fractals. The unity of basis constructions and their expansions is emphasized as the starting point for the development of bases that are computationally efficient for use in several areas from wavelets to fractals.

The book brings together tools from engineering and math, especially from signal- and image processing, and from harmonic analysis and operator theory. The presentation is aimed at graduate students, as well as users from a diverse spectrum of applications.

Key features:

 • A hands-on approach for students, including tutorials and numerous exercises;

 • Excellent motivation throughout;

 • New pedagogical features: glossary of terms, their use in mathematics and in engineering, help forcross-audiences, image processing, visual presentation of key algorithms, structure and geometry of big matrix computations, explanation of uses of the theory in applications outside of mathematics;

 • Includes more than 50 figures with captions, illustrating the main ideas, plus engineering diagrams, graphic renditions of algorithms, and separate illustrations;

 • Separate sections in the book explain engineering terms to mathematicians, and operator theory to engineers;

 • Each chapter concludes with a helpful guide to the literature allowing students to follow up on the topics in the book.

Palle E.T. Jorgensen is a Professor of Mathematics at the University of Iowa. This book is based in part on interdisciplinary courses that he has taught over the last several years, and on his work with his current and former students. His most recent book was written jointly with Ola Bratteli and is entitled Wavelets through a LookingGlass, ©2002 Birkhäuser Boston.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2010
• Sprache: Englisch
• ISBN 10: 1441921265
• ISBN 13: 9781441921260
• Einband: Taschenbuch
• Anzahl der Seiten: 332
• Kontakt zum Hersteller: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Deutschland