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Differentiable Operators and Nonlinear Equations (Hardcover, 1994 ed.)
Loot Price: R3,039
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Differentiable Operators and Nonlinear Equations (Hardcover, 1994 ed.)
Series: Operator Theory: Advances and Applications, 66
Expected to ship within 10 - 15 working days
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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).
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