UID:
edocfu_9958353941502883
Format:
1 online resource(xvi,497p.) :
,
illustrations.
Edition:
Electronic reproduction. Berlin/Boston : De Gruyter. Mode of access: World Wide Web.
Edition:
System requirements: Web browser.
Edition:
Access may be restricted to users at subscribing institutions.
ISBN:
9783110258998
Series Statement:
De Gruyter Series in Nonlinear Analysis and Applications; 19
Content:
This bookis aboutthe subject of higher smoothness in separable real Banach spaces.It brings together several angles of view on polynomials, both in finite and infinite setting.Also a rather thorough and systematic view of the more recent results, and the authors work is given. The book revolves around two main broad questions: What is the best smoothness of a given Banach space, and its structural consequences? How large is a supply of smooth functions in the sense of approximating continuous functions in the uniform topology, i.e. how does the Stone-Weierstrass theorem generalize into infinite dimension where measure and compactness are not available? The subject of infinite dimensional real higher smoothness is treatedherefor the first time in full detail, therefore this book may also serve as a reference book.
Note:
Frontmatter --
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Contents --
,
Introduction --
,
Chapter 1. Fundamental properties of smoothness --
,
Chapter 2. Basic properties of polynomials on R --
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Chapter 3. Weak continuity of polynomials and estimates of coefficients --
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Chapter 4. Asymptotic properties of polynomials --
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Chapter 5. Smoothness and structure --
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Chapter 6. Structural behaviour of smooth mappings --
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Chapter 7. Smooth approximation --
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Bibliography --
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Notation --
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Index.
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Also available in print edition.
,
In English.
Additional Edition:
ISBN 9783110258981
Additional Edition:
ISBN 9783112203859
Language:
English
DOI:
10.1515/9783110258998
URL:
https://doi.org/10.1515/9783110258998
