Differentiable Operators and Nonlinear Equations: 66 (Operator Theory: Advances and Applications, 66) - Softcover

Khatskevich, Victor; Shoiykhet, David

Softcover

ISBN 10: 3034896581 ISBN 13: 9783034896580

Publisher: Birkhäuser, 2012

Synopsis

We have considered writing the present book for a long time, since the lack of a sufficiently complete textbook about complex analysis in infinite dimensional spaces was apparent. There are, however, some separate topics on this subject covered in the mathematical literature. For instance, the elementary theory of holomorphic vector- functions.and mappings on Banach spaces is presented in the monographs of E. Hille and R. Phillips [1] and L. Schwartz [1], whereas some results on Banach algebras of holomorphic functions and holomorphic operator-functions are discussed in the books of W. Rudin [1] and T. Kato [1]. Apparently, the need to study holomorphic mappings in infinite dimensional spaces arose for the first time in connection with the development of nonlinear anal- ysis. A systematic study of integral equations with an analytic nonlinear part was started at the end ofthe 19th and the beginning ofthe 20th centuries by A. Liapunov, E. Schmidt, A. Nekrasov and others. Their research work was directed towards the theory of nonlinear waves and used mainly the undetermined coefficients and the majorant power series methods. The most complete presentation of these methods comes from N. Nazarov. In the forties and fifties the interest in Liapunov's and Schmidt's analytic methods diminished temporarily due to the appearence of variational calculus meth- ods (M. Golomb, A. Hammerstein and others) and also to the rapid development of the mapping degree theory (J. Leray, J. Schauder, G. Birkhoff, O. Kellog and others).

Edition details

• Publisher: Birkhäuser
• Publication date: 2012
• Language: English
• ISBN 10: 3034896581
• ISBN 13: 9783034896580
• Binding: Paperback
• Number of pages: 294