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Analysis in Banach Spaces

Tuomas Hytoenen, Jan van Neerven, Mark Veraar and Lutz Weis


  • Hardcover
    $232.30
PUBLISHED: 22nd February 2018
ISBN: 9783319698076
ANNOTATION:
This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory.
Analysis in Banach Spaces
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OTHER FORMATS:
  • Hardcover
    $232.30
PUBLISHED: 22nd February 2018
ISBN: 9783319698076
ANNOTATION:
This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory.

Annotation

This second volume of Analysis in Banach Spaces, Probabilistic Methods and Operator Theory, is the successor to Volume I, Martingales and Littlewood-Paley Theory.

Publisher 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.

Author Biography

Tuomas Hytoenen is Professor at the University of Helsinki. A leading expert in Harmonic Analysis with over 60 research papers, he was educated at Helsinki University of Technology and spent a postdoc year at Delft University of Technology. He received a European Research Council Starting Grant in 2011 and gave an invited address to the International Congress of Mathematicians in 2014.

Jan van Neerven is Professor of Analysis at Delft University of Technology. Author of more than 100 research papers and two monographs, he is a leading expert in Operator Theory and Stochastic Analysis. He held post-doctoral positions at Caltech and Tubingen University. He was awarded a Human Capital and Mobility fellowship, a fellowship of the Royal Dutch Academy of Arts and Sciences, and VIDI and VICI subsidies from the Netherlands Organisation for Scientific Research.

Mark Veraar is Associate Professor at Delft University of Technology. Author of over 40 research papers, he is a leading researcher in the theory of evolution equations and stochastic partial differential equations. He held post-doctoral positions at the Universities of Warsaw and Karlsruhe, the latter with a Alexander von Humboldt Fellowship. He is the recipient of VENI and VIDI grants from the Netherlands Organisation for Scientific Research.

Lutz Weis, a Professor at Karlsruhe Institute of Technology, is a senior researcher in operator theory and evolution equations. He has published over 80 research papers and a monograph. Since receiving his PhD from University of Bonn, he was a professor at Louisiana State University and visiting professor at TU Berlin as well as Universities of Kiel, South Carolina and Minnesota. He organized a Marie Curie training site and is currently a member of a DFG Graduiertenkolleg.

Table of 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.

Review

"The book will become an invaluable reference for graduate students and researchers. Those interested in functional analysis, harmonic analysis and stochastic analysis will appreciate the detailed treatment of the theory of R-boundedness, radonifying operators and holomorphic functional calculus developed over the last 20 years." (Oscar Blasco, zbMATH 1402.46002, 2019)

Product Details

Publisher
Springer International Publishing AG
Series
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Edition
1st
ISBN-10
3319698079
ISBN-13
9783319698076
Format
Hardcover
Subtitle
Volume II: Probabilistic Methods and Operator Theory
Country of Publication
Switzerland
Pages
616
Author
Tuomas Hytoenen, Jan van Neerven, Mark Veraar, Lutz Weis
Year
2018
Illustrations
7 Illustrations, black and white; XXIII, 616 p. 7 illus.
Publication Date
2018-02-22