Award-winning monograph of the Ferran Sunyer i Balaguer Prize 2004.

This book studies regularity properties of Mumford-Shah minimizers. The Mumford-Shah functional was introduced in the 1980s as a tool for automatic image segmentation, but its study gave rise to many interesting questions of analysis and geometric measure theory. The main object under scrutiny is a free boundary K where the minimizer may have jumps. The book presents an extensive description of the known regularity properties of the singular sets K, and the techniques to get them. Some time is spent on the C1 regularity theorem (with an essentially unpublished proof in dimension 2), but a good part of the book is devoted to applications of A. Bonnet's monotonicity and blow-up techniques. In particular, global minimizers in the plane are studied in full detail.
The book is largely self-contained and should be accessible to graduate students in analysis.The core of the book is composed of regularity results that were proved in the last ten years and which are presented in a more detailed and unified way.

Wavelets are a recently developed tool for the analysis and synthesis of functions; their simplicity, versatility and precision makes them valuable in many branches of applied mathematics. The book begins with an introduction to the theory of wavelets and limits itself to the detailed construction of various orthonormal bases of wavelets. A second part centers on a criterion for the L2-boundedness of singular integral operators: the T(b)-theorem. It contains a full proof of that theorem. It contains a full proof of that theorem, and a few of the most striking applications (mostly to the Cauchy integral). The third part is a survey of recent attempts to understand the geometry of subsets of Rn on which analogues of the Cauchy kernel define bounded operators. The book was conceived for a graduate student, or researcher, with a primary interest in analysis (and preferably some knowledge of harmonic analysis and seeking an understanding of some of the new "real-variable methods" used in harmonic analysis.

According to Eric Clapton, John Mayer, and the late Stevie Ray Vaughn, Buddy Guy is the greatest blues guitarist of all time. An enormous influence on these musicians as well as Jimi Hendrix, Jimmy Page, and Jeff Beck, he is the living embodiment of Chicago blues. Guy's epic story stands at the absolute nexus of modern blues. He came to Chicago from rural Louisiana in the fifties,the very moment when urban blues were electrifying our culture. He was a regular session player at Chess Records. Willie Dixon was his mentor. He was a sideman in the bands of Muddy Waters and Howlin' Wolf. He and Junior Wells formed a band of their own. In the sixties, he became a recording star in his own right. When I Left Home tells Guy's picaresque story in his own unique voice, that of a storyteller who remembers everything, including blues masters in their prime and the exploding, evolving culture of music that happened all around him.

New perspectives on an important era in Mesoamerican history This volume examines shifting social identities, lived experiences, and networks of interaction in Mexico during the Mesoamerican Formative period (2000 BCE-250 CE), an era that helped produce some of the world's most renowned complex civilizations. The chapters offer significant data, innovative methodologies, and novel perspectives on Mexican archaeology. Using diverse and non-traditional theoretical approaches, contributors discuss interregional relationships and the exchange of ideas in contexts ranging from the Gulf Coast Olmec region to the site of Tlatilco in Central Mexico to the often-overlooked cultures of the far western states. Their essays explore identity formation, cosmological perspectives, the first hints of social complexity, the underpinnings of Formative period economies, and the sensorial implications of sociocultural change. Identities, Experience, and Change in Early Mexican Villages is one of the first volumes to address the entirety of this rich and complex era and region, offering a new and holistic view. Through a wealth of exciting interpretations from international senior and emerging scholars, this volume shows the strong influence of cultural exchange as well as the compelling individuality of local and regional contexts over two thousand years of history.

This book proposes new notions of coherent geometric structure. Fractal patterns have emerged in many contexts, but what exactly is a "pattern" and what is not? How can one make precise the structures lying within objects and the relationships between them? The foundations laid herein provide a fresh approach to a familiar field. From this emerges a wide range of open problems, large and small, and a variety of examples with diverse connections to other parts of mathematics. One of the main features of the present text is that the basic framework is completely new. This makes it easier for people to get into the field. There are many open problems, with plenty of opportunities that are likely to be close at hand, particularly as concerns the exploration of examples. On the other hand the general framework is quite broad and provides the possibility for future discoveries of some magnitude. Fractual geometries can arise in many different ways mathematically, but there is not so much general language for making comparisons. This book provides some tools for doing this, and a place where researchers in different areas can find common ground and basic information.