It is well known that a wealth of problems of different nature, applied as well as purely theoretic, can be reduced to the study of elliptic equations and their eigen-values. During the years many books and articles have been published on this topic, considering spectral properties of elliptic differential operators from different points of view. This is one more book on these properties. This book is devoted to the study of some classical problems of the spectral theory of elliptic differential equations. The reader will find hardly any intersections with the books of Shubin [Sh] or Rempel-Schulze [ReSch] or with the works cited there. This book also has no general information in common with the books by Egorov and Shubin [EgShu], which also deal with spectral properties of elliptic operators. There is nothing here on oblique derivative problems; the reader will meet no pseudodifferential operators. The main subject of the book is the estimates of eigenvalues, especially of the first one, and of eigenfunctions of elliptic operators. The considered problems have in common the approach consisting of the application of the variational principle and some a priori estimates, usually in Sobolev spaces. In many cases, impor tant for physics and mechanics, as well as for geometry and analysis, this rather elementary approach allows one to obtain sharp results.
For over five hundred years the Russians wondered what kind of people their Arctic and sub-Arctic subjects were. "They have mouths between their shoulders and eyes in their chests," reported a fifteenth-century tale. "They rove around, live of their own free will, and beat the Russian people," complained a seventeenth-century Cossack. "Their actions are exceedingly rude. They do not take off their hats and do not bow to each other," huffed an eighteenth-century scholar. They are "children of nature" and "guardians of ecological balance," rhapsodized early nineteenth-century and late twentieth-century romantics. Even the Bolsheviks, who categorized the circumpolar foragers as "authentic proletarians," were repeatedly puzzled by the "peoples from the late Neolithic period who, by virtue of their extreme backwardness, cannot keep up either economically or culturally with the furious speed of the emerging socialist society."Whether described as brutes, aliens, or endangered indigenous populations, the so-called small peoples of the north have consistently remained a point of contrast for speculations on Russian identity and a convenient testing ground for policies and images that grew out of these speculations. In Arctic Mirrors, a vividly rendered history of circumpolar peoples in the Russian empire and the Russian mind, Yuri Slezkine offers the first in-depth interpretation of this relationship. No other book in any language links the history of a colonized non-Russian people to the full sweep of Russian intellectual and cultural history. Enhancing his account with vintage prints and photographs, Slezkine reenacts the procession of Russian fur traders, missionaries, tsarist bureaucrats, radical intellectuals, professional ethnographers, and commissars who struggled to reform and conceptualize this most "alien" of their subject populations.Slezkine reconstructs from a vast range of sources the successive official policies and prevailing attitudes toward the northern peoples, interweaving the resonant narratives of Russian and indigenous contemporaries with the extravagant images of popular Russian fiction. As he examines the many ironies and ambivalences involved in successive Russian attempts to overcome northern—and hence their own—otherness, Slezkine explores the wider issues of ethnic identity, cultural change, nationalist rhetoric, and not-so European colonialism.
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