Iouri Egorov; Bert-Wolfgang Schulze Pseudo-Differential Operators, Singularities, Applications 9783034898201

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Автор: Iouri Egorov; Bert-Wolfgang Schulze
Название: Pseudo-Differential Operators, Singularities, Applications
ISBN: 9783034898201
Издательство: Springer
Классификация:

Основы высшей математики и математический анализ

ISBN-10: 3034898207
Обложка/Формат: Paperback
Страницы: 353
Вес: 0.59 кг.
Дата издания: 16.10.2012
Серия: Operator Theory: Advances and Applications
Язык: English
Размер: 244 x 170 x 20
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание: Pseudo-differential operators belong to the most powerful tools in the analysis of partial differential equations. Basic achievements in the early sixties have initiated a completely new understanding of many old and important problems in analy- sis and mathematical physics. The standard calculus of pseudo-differential and Fourier integral operators may today be considered as classical. The development has been continuous since the early days of the first essential applications to ellip- ticity, index theory, parametrices and propagation of singularities for non-elliptic operators, boundary-value problems, and spectral theory. The basic ideas of the calculus go back to Giraud, Calderon, Zygmund, Mikhlin, Agranovich, Dynin, Vishik, Eskin, and Maslov. Subsequent progress was greatly stimulated by the classical works of Kohn, Nirenberg and Hormander. In recent years there developed a new vital interest in the ideas of micro- local analysis in connection with analogous fields of applications over spaces with singularities, e.g. conical points, edges, corners, and higher singularities. The index theory for manifolds with singularities became an enormous challenge for analysists to invent an adequate concept of ellipticity, based on corresponding symbolic structures. Note that index theory was another source of ideas for the later development of the theory of pseudo-differential operators. Let us mention, in particular, the fundamental contributions by Gelfand, Atiyah, Singer, and Bott.

Pseudo-Differential Operators, Singularities, Applications, Iouri Egorov; Bert-Wolfgang Schulze