Ishtiaq, Amna: Grid points and generalized discrepancies on the d-dimensional ball. 2018
Inhalt
- Acknowledgements
- Abstract
- Zusammenfassung
- Introduction
- Contents
- Chapter 1 - Preliminaries
- 1.1 Notations
- 1.2 Orthogonal Polynomials
- 1.3 Spherical Harmonics
- 1.4 Orthonormal Systems on the Ball
- 1.5 Statistical Preliminaries
- Chapter 2 - Quadrature Points on the Ball
- 2.1 Pseudodifferential Operators on the Ball
- 2.2 Generalized Discrepancy
- 2.3 Weighted Grid Point Approximation
- 2.4 Operators and Eigenvalues
- Chapter 3 - Construction of Point Grids and Discrepancy Estimates
- Chapter 4 - Lower Discrepancy Point Grids
- Chapter 5 - Statistical Computation
- Chapter 6 - Generalization to Higher Dimensions
- 6.1 Basic Notations
- 6.2 Spherical Harmonics in d Dimensions
- 6.3 Orthonormal Systems in d Dimensions
- 6.4 Differential Operators for Orthonormal Systems on BdR
- 6.5 Sobolev Space on BdR
- 6.6 Discrepancy in Higher Dimensions
- 6.7 Numerical Properties of the Generalized Discrepancy
- Chapter 7 - Numerical Tests: Numerical Integration
- Chapter 8 - Conclusions and Outlook
- Bibliography