Pseudodifferential Operators and Spectral Theory - Rilegato

Shubin, M.

Rilegato

ISBN 10: 3540136215 ISBN 13: 9783540136217

Casa editrice: Springer-Verlag Berlin and Heidelberg GmbH & Co. K, 1987

Riassunto

The theory of pseudo differential operators (abbreviated PD~) is compara­ tively young; in its modern form it was created in the mid-sixties. The progress achieved with its help, however, has been so essential that without PD~ it would indeed be difficult to picture modern analysis and mathematical physics. PD~ are of particular importance in the study of elliptic equations. Even the simplest operations on elliptic operators (e. g. taking the inverse or the square root) lead out of the class of differential operators but will, under reasonable assumptions, preserve the class of PD~. A significant role is played by PD~ in the index theory for elliptic operators, where PD~ are needed to extend the class of possible deformations of an operator. PD~ appear naturally in the reduction to the boundary for any elliptic boundary problem. In this way, PD~ arise not as an end-in-themselves, but as a powerful and natural tool for the study of partial differential operators (first and foremost elliptic and hypo elliptic ones). In many cases, PD~ allow us not only to establish new theorems but also to have a fresh look at old ones and thereby obtain simpler and more transparent formulations of already known facts. This is, for instance, the case in the theory of Sobolev spaces. A natural generalization of PD~ are the Fourier integral operators (abbreviatedFIO), the first version ofwhich was the Maslov canonical operator.

Su questa edizione

• Editore: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
• Data di pubblicazione: 1987
• ISBN 10: 3540136215
• ISBN 13: 9783540136217
• Rilegatura: Copertina rigida
• Numero edizione: 1
• Numero di pagine: 288