Analysis in Banach Spaces : Volume II: Probabilistic Methods and Operator Theory (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / a Series of Modern Surveys in Mathematics)

Hytönen, Tuomas/ van Neerven, Jan/ Veraar, Mark

Springer International Publishing AG（2018/02発売）

• 製本 Hardcover:ハードカバー版／ページ数 616 p.
• 言語 ENG
• 商品コード 9783319698076

Full Description

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory. It presents a thorough study of the fundamental randomisation techniques and the operator-theoretic aspects of the theory. The first two chapters address the relevant classical background from the theory of Banach spaces, including notions like type, cotype, K-convexity and contraction principles. In turn, the next two chapters provide a detailed treatment of the theory of R-boundedness and Banach space valued square functions developed over the last 20 years. In the last chapter, this content is applied to develop the holomorphic functional calculus of sectorial and bi-sectorial operators in Banach spaces. Given its breadth of coverage, this book will be an invaluable reference to graduate students and researchers interested in functional analysis, harmonic analysis, spectral theory, stochastic analysis, and the operator-theoretic approach to deterministic and stochastic evolution equations. 

Contents

6.Random sums.-7.Type, cotype, and related properties.- 8.R-boundedness.- 9.Square functions and radonifying operators.- 11.The H1-functional calculus.- P.Open problems.- E.Probability theory.- F Banach lattices.- G Semigroups of linear operators.- H.Holomorphic functions on the strip.- I.Muckenhoupt weights.- References.- Index.