The series is devoted to the publication of high-level monographs which cover the whole spectrum of current nonlinear analysis and applications in various fields, such as optimization, control theory, systems theory, mechanics, engineering, and other sciences. One of its main objectives is to make available to the professional community expositions of results and foundations of methods that play an important role in both the theory and applications of nonlinear analysis. Contributions which are on the borderline of nonlinear analysis and related fields and which stimulate further research at the crossroads of these areas are particularly welcome.
Editor-in-Chief
Dr. Vesselin Vatchev, USA
Honorary and Advisory Editors
Catherine Bandle, Basel, Switzerland
Jiguang Bao, Beijing, China
Avner Friedman, Columbus, Ohio, USA
Manuel del Pino, Bath, UK, and Santiago, Chile
Mikio Kato, Nagano, Japan
Guozhen Lu, Storrs, CT, USA
Wojciech Kryszewski, Lodz University of Technology, Poland
Vicentiu D. Radulescu, Kraków, Poland
Simeon Reich, Haifa, Israel
Please submit book proposals to Jürgen Appell.
Titles in planning include
Ireneo Peral Alonso and Fernando Soria, Elliptic and Parabolic Equations Involving the Hardy-Leray Potential (2020)
Cyril Tintarev, Profile Decompositions and Cocompactness: Functional-Analytic Theory of Concentration Compactness (2020)
Takashi Suzuki, Semilinear Elliptic Equations: Classical and Modern Theories (2021)
Autorentext
Petr Hájek, Academy of Sciences of the Czech Republic, Prague, Czech Republic; Michal Johanis, Charles University, Prague, Czech Republic.
Klappentext
This book is about the 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 treated here for the first time in full detail, therefore this book may also serve as a reference book.