David Edmunds Livres

Classical Sobolev spaces, based on Lebesgue spaces on an underlying domain with smooth boundary, are not only of considerable intrinsic interest but have for many years proved to be indispensible in the study of partial differential equations and variational problems. Many developments of the basic theory since its inception arise in response to concrete problems, for example, with the (ubiquitous) sets with fractal boundaries. The theory will probably enjoy substantial further growth, but even now a connected account of the mature parts of it makes a useful addition to the literature. Accordingly, the main themes of this book are Banach spaces and spaces of Sobolev type based on them; integral operators of Hardy type on intervals and on trees; and the distribution of the approximation numbers (singular numbers in the Hilbert space case) of embeddings of Sobolev spaces based on generalised ridged domains. This timely book will be of interest to all those concerned with the partial differential equations and their ramifications. A prerequisite for reading it is a good graduate course in real analysis.

The book deals with the representation in series form of compact linear operators acting between Banach spaces, and provides an analogue of the classical Hilbert space results of this nature that have their roots in the work of D. Hilbert, F. Riesz and E. Schmidt. The representation involves a recursively obtained sequence of points on the unit sphere of the initial space and a corresponding sequence of positive numbers that correspond to the eigenvectors and eigenvalues of the map in the Hilbert space case. The lack of orthogonality is partially compensated by the systematic use of polar sets. There are applications to the p -Laplacian and similar nonlinear partial differential equations. Preliminary material is presented in the first chapter, the main results being established in Chapter 2. The final chapter is devoted to the problems encountered when trying to represent non-compact maps.

In this engaging narrative, acclaimed historian R. David Edmunds combines careful research with creative storytelling to give voice to indigenous individuals and families and to illustrate the impact of pivotal events on their lives. A nonfiction account accompanies each narrative to provide necessary historical and cultural context.

Throughout history, Indian leaders and their methods of leadership have both perplexed and fascinated other Americans. Because war chiefs played leading roles in the confrontations with whites, it is they who most often emerge from the pages of history. But there were many other leaders who sought security for their tribesmen in accommodation or friendship with the Anglo-Americans. Indeed, as the twelve subjects whose careers are examined in this collection illustrate, Indian political leadership has manifested itself in a wide variety of patterns. Spanning the period from colonial times to the present, the essays are devoted to Old Briton, Joseph Brant (or, Thayendenegea), Alexander McGillivray, Red Bird, John Ross, Satanta, Washakie, Sitting Bull, Quanah Parker, Dennis Bushyhead, Carlos Montezuma, and Peter MacDonald.

In the early 1800s, when control of the Old Northwest had not yet been assured to the United States, the Shawnee leaders Tecumseh and his brother Tenskwatawa, the Shawnee Prophet, led an intertribal movement culminating at the Battle of Tippecanoe and the Battle of the Thames. Historians have portrayed Tecumseh, the war leader, as the key figure in forging the intertribal confederacy. In this full-length biography of Tenskwatawa, R. David Edmunds shows that, to the contrary, the Shawnee Prophet initiated and for much of the period dominated the movement, providing a set of religious beliefs and ceremonies that revived the tribes' fading power and cohesion.