Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces

Fréchet Differentiability of Lipschitz Functions and Porous Sets in Banach Spaces

eBook - 2012
Rate this:

This book makes a significant inroad into the unexpectedly difficult question of existence of Fréchet derivatives of Lipschitz maps of Banach spaces into higher dimensional spaces. Because the question turns out to be closely related to porous sets in Banach spaces, it provides a bridge between descriptive set theory and the classical topic of existence of derivatives of vector-valued Lipschitz functions. The topic is relevant to classical analysis and descriptive set theory on Banach spaces. The book opens several new research directions in this area of geometric nonlinear functional analysis.


The new methods developed here include a game approach to perturbational variational principles that is of independent interest. Detailed explanation of the underlying ideas and motivation behind the proofs of the new results on Fréchet differentiability of vector-valued functions should make these arguments accessible to a wider audience. The most important special case of the differentiability results, that Lipschitz mappings from a Hilbert space into the plane have points of Fréchet differentiability, is given its own chapter with a proof that is independent of much of the work done to prove more general results. The book raises several open questions concerning its two main topics.

Publisher: Princeton : Princeton University Press, 2012.
ISBN: 9781400842698
9780691153568
9780691153551
Characteristics: 1 online resource (ix, 425 pages).

Opinion

From the critics


Community Activity

Comment

Add a Comment

There are no comments for this title yet.

Age

Add Age Suitability

There are no ages for this title yet.

Summary

Add a Summary

There are no summaries for this title yet.

Notices

Add Notices

There are no notices for this title yet.

Quotes

Add a Quote

There are no quotes for this title yet.

Explore Further

Subject Headings

  Loading...

Find it at KCLibrary

  Loading...
[]
[]
To Top