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Published in:
2020 | OriginalPaper | Chapter
Infinite-Dimensional Analysis
Authors : Vladimir I. Bogachev, Oleg G. Smolyanov
Published in: Real and Functional Analysis
Publisher: Springer International Publishing
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In this chapter we discuss foundations of differential calculus in infinite–dimensional spaces and some related questions. In the finite–dimensional case there are two different types of differentiability: differentiability at a point based on the consideration of increments of the function and also a global differentiability based on the consideration of the derivative as some independent object (as this is done in the theory of distributions and in the theory of Sobolev spaces).