This book provides a systematic development of the Rubio de Francia theory of extrapolation, its many generalizations and its applications to one and two-weight norm inequalities. The book is based upon a new and elementary proof of the classical extrapolation theorem that fully develops the power of the Rubio de Francia iteration algorithm. This technique allows us to give a unified presentation of the theory and to give important generalizations to Banach function spaces and to two-weight inequalities. We provide many applications to the classical operators of harmonic analysis to illustrate our approach, giving new and simpler proofs of known results and proving new theorems. The book is intended for advanced graduate students and researchers in the area of weighted norm inequalities, as well as for mathematicians who want to apply extrapolation to other areas such as partial differential equations.
This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest since the early 1990s because of their connection with the calculus of variations and partial differential equations with nonstandard growth conditions, and for their applications to problems in physics and image processing. The book begins with the development of the basic function space properties. It avoids a more abstract, functional analysis approach, instead emphasizing an hands-on approach that makes clear the similarities and differences between the variable and classical Lebesgue spaces. The subsequent chapters are devoted to harmonic analysis on variable Lebesgue spaces. The theory of the Hardy-Littlewood maximal operator is completely developed, and the connections between variable Lebesgue spaces and the weighted norm inequalities are introduced. The other important operators in harmonic analysis - singular integrals, Riesz potentials, and approximate identities - are treated using a powerful generalization of the Rubio de Francia theory of extrapolation from the theory of weighted norm inequalities. The final chapter applies the results from previous chapters to prove basic results about variable Sobolev spaces.
The Stieltjes Integral provides a detailed, rigorous treatment of the Stieltjes integral. This integral is a generalization of the Riemann and Darboux integrals of calculus and undergraduate analysis, and can serve as a bridge between classical and modern analysis. It has applications in many areas, including number theory, statistics, physics, and finance. It begins with the Darboux integral, builds the theory of functions of bounded variation, and then develops the Stieltjes integral. It culminates with a proof of the Riesz representation theorem as an application of the Stieltjes integral. For much of the 20th century the Stjeltjes integral was a standard part of the undergraduate or beginning graduate student sequence in analysis. However, the typical mathematics curriculum has changed at many institutions, and the Stieltjes integral has become less common in undergraduate textbooks and analysis courses. This book seeks to address this by offering an accessible treatment of the subject to students who have had a one semester course in analysis. This book is suitable for a second semester course in analysis, and also for independent study or as the foundation for a senior thesis or Masters project. Features: Written to be rigorous without sacrificing readability. Accessible to undergraduate students who have taken a one-semester course on real analysis. Contains a large number of exercises from routine to challenging.
This book targets graduate students and researchers who want to learn about Lebesgue spaces and solutions to hyperbolic equations. It is divided into two parts. Part 1 provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces like the classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally from the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. After an introduction that sketches history and motivation, the authors develop the function space properties of variable Lebesgue spaces; proofs are modeled on the classical theory. Subsequently, the Hardy-Littlewood maximal operator is discussed. In the last chapter, other operators from harmonic analysis are considered, such as convolution operators and singular integrals. The text is mostly self-contained, with only some more technical proofs and background material omitted. Part 2 gives an overview of the asymptotic properties of solutions to hyperbolic equations and systems with time-dependent coefficients. First, an overview of known results is given for general scalar hyperbolic equations of higher order with constant coefficients. Then strongly hyperbolic systems with time-dependent coefficients are considered. A feature of the described approach is that oscillations in coefficients are allowed. Propagators for the Cauchy problems are constructed as oscillatory integrals by working in appropriate time-frequency symbol classes. A number of examples is considered and the sharpness of results is discussed. An exemplary treatment of dissipative terms shows how effective lower order terms can change asymptotic properties and thus complements the exposition.
Hibis Temple, tucked away in the remote Khargeh Oasis, contains the longest monumental hymns to Amun-Re ever carved in hieroglyphs. These religious texts, inscribed during the reign of Darius I, drew upon a large variety of New Kingdom sources, and later they served as sources for the Graeco-Roman hymns at Esna Temple. As such, the hymns to Amun-Re from Hibis are excellently suited for studying Egyptian theology during the Persian Period, on the eve of the supposed "new theology" created by the Graeco-Roman priesthood. This new study, the first extensive commentary on the five liturgically connected hymns, features new translations with detailed notes. The book also considers dominant theological themes present in the texts, including the concept of "Amun within the Iris.
Prehistoric Subsistence on the Southern New England Coast examines long-term trends in prehistoric subsistence in the Narragensett Bay region of Southern New England. The results suggest that, unlike other areas of Eastern north America, specialized agriculutral economies did not develop in this region prior to European contact. The book is accessible to both the general reader as well as scholars and students interested in consulting the original data for their own research and analysis. * * Incorporates original research in palynology and geomorphology in to an archaeological study* Presents a study of modern shellfish growth that is used to interpret the archaeological remains found at Greenwich Cove* Uses numerous animal species to determine site seasonality
Government is broke. The 2004 federal deficit is the highest in U.S. history. The states have suffered three years of record shortfalls. Cities, counties, and school districts are laying off policemen and teachers, closing schools, and cutting services. But the fiscal pain won't go away, and the bankrupt ideologies of left and right offer little guidance.The Price of Government presents a radically different approach to budgeting -- one that focuses on buying results for citizens rather than cutting or adding to last year's spending programs. It advocates consolidation, competition, customer choice, and a relentless focus on results to save millions while improving public services.
The theory of Lebesgue and Sobolev spaces with variable integrability is experiencing a steady expansion, and is the subject of much vigorous research by functional analysts, function-space analysts and specialists in nonlinear analysis. These spaces have attracted attention not only because of their intrinsic mathematical importance as natural, interesting examples of non-rearrangement-invariant function spaces but also in view of their applications, which include the mathematical modeling of electrorheological fluids and image restoration.The main focus of this book is to provide a solid functional-analytic background for the study of differential operators on spaces with variable integrability. It includes some novel stability phenomena which the authors have recently discovered.At the present time, this is the only book which focuses systematically on differential operators on spaces with variable integrability. The authors present a concise, natural introduction to the basic material and steadily move toward differential operators on these spaces, leading the reader quickly to current research topics.
In Renewing Royal Imagery: Akhenaten and Family in the Amarna Tombs, Arlette David offers a systematic analysis of the visual presentation of ancient Egyptian kingship during Akhenaten's reign (circa 1350 B.C.) in the elite tombs of his new capital.
The orthodox view of slavery in the ancient Mediterranean holds that Greece and Rome were its only 'genuine slave societies', that is, societies in which slave labour contributed significantly to the economy and underpinned the wealth of elites. Other societies, traditionally labelled 'societies with slaves', are thought to have made little use of slave labour and therefore have been largely ignored in recent scholarship. This volume presents a radically different view of the ancient Eastern Mediterranean world, showing that elite exploitation of slave labour in Greece and the Near East shared some fundamental similarities, although the degree of elite dependence on slaves varied from region to region. Whilst slavery was indeed particularly highly developed in Greece and Rome, it was also economically entrenched in Carthage, and played a not insignificant role in the affairs of elites in Israel, Assyria, Babylonia, and Persia. The differing degrees to which Eastern Mediterranean elites exploited slave labour represents the outcome of a complex interplay between cultural, economic, political, geographical, and demographic factors. Proceeding on a regional basis, this book tracks the ways in which local conditions shaped a wide variety of Greek and Near Eastern slave systems, and how the legal architecture of slavery in individual regions was altered and adapted to accommodate these needs. The result is a nuanced exploration of the economic underpinnings of Greek elite culture that sets its reliance on slavery within a broader historical context and sheds light on the complex circumstances from which it emerged.
Description of the archaeological excavation and analysis of the Kugaluk site located near Eskimo Lakes east of Tuktoyaktuk, Northwest Territories. The area was inhabited by the Nuvorugmiut, one of the branches of the Mackenzie Inuit who seasonally exploited the caribou and whale and may have had a stratified social structure.
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