Operator-Adapted Wavelets, Fast Solvers, and Numerical Homogenization From a Game Theoretic Approach to Numerical Approximation and Algorithm Design
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Reading Guide
- 1 Introduction
- Part I The Sobolev Space Setting
- Part II The Game Theoretic Approach
- Part III The Banach Space Setting
- Part IV Game Theoretic Approach on Banach Spaces
- 17 Gaussian Measures, Cylinder Measures, and Fields on B
- 18 Optimal Recovery Games on B
- 19 Game Theoretic Interpretation of Gamblets
- 20 Survey of Statistical Numerical Approximation
- Part V Applications, Developments, and Open Problems
- Part VI Appendix
- Bibliography
- Algorithms
- Glossary
- Nomenclature
- Index
- Identities
17 - Gaussian Measures, Cylinder Measures, and Fields on B
from Part IV - Game Theoretic Approach on Banach Spaces
Published online by Cambridge University Press: 10 October 2019
Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- Acknowledgements
- Reading Guide
- 1 Introduction
- Part I The Sobolev Space Setting
- Part II The Game Theoretic Approach
- Part III The Banach Space Setting
- Part IV Game Theoretic Approach on Banach Spaces
- 17 Gaussian Measures, Cylinder Measures, and Fields on B
- 18 Optimal Recovery Games on B
- 19 Game Theoretic Interpretation of Gamblets
- 20 Survey of Statistical Numerical Approximation
- Part V Applications, Developments, and Open Problems
- Part VI Appendix
- Bibliography
- Algorithms
- Glossary
- Nomenclature
- Index
- Identities
Summary
This chapter extends the presentation ofGaussian measures, cylinder measures, and fields fromSobolev spaces to Banach spaceswith quadratic energynorm. The relationship between weak distributions and cylinder measures is elucidated as is the relationship between Gaussian cylinder measures and Gaussian fields.
Keywords
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- Operator-Adapted Wavelets, Fast Solvers, and Numerical HomogenizationFrom a Game Theoretic Approach to Numerical Approximation and Algorithm Design, pp. 347 - 359Publisher: Cambridge University PressPrint publication year: 2019