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Analysis and Probability

Wavelets, Signals, Fractals

Palle E. T. Jorgensen (Autor)

Buch | Hardcover

280 Seiten

2006 | 2006 ed.
Springer-Verlag New York Inc.
978-0-387-29519-0 (ISBN)

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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.

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.

Reihe/Serie	Graduate Texts in Mathematics ; 234
Illustrationen	B Treadway
Zusatzinfo	XLVIII, 280 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Themenwelt	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	0-387-29519-4 / 0387295194
ISBN-13	978-0-387-29519-0 / 9780387295190
Zustand	Neuware