Book contents
- Frontmatter
- Epigraph
- Contents
- Foreword
- Preface
- Part I Fourier Series
- Part II Some Differential Equations
- Part III Orthogonal Series
- 32 Mean square approximation I
- 33 Mean square approximation II
- 34 Mean square convergence
- 35 The isoperimetric problem I
- 36 The isoperimetric problem II
- 37 The Sturm—Liouville equation I
- 38 Liouville
- 39 The Sturm—Liouville equation II
- 40 Orthogonal polynomials
- 41 Gaussian quadrature
- 42 Linkages
- 43 Tchebychev and uniform approximation I
- 44 The existence of the best approximation
- 45 Tchebychev and uniform approximation II
- Part IV Fourier Transforms
- Part V Further Developments
- Part VI Other Directions
- Appendix A The circle T
- Appendix B Continuous function on closed bounded sets
- Appendix C Weakening hypotheses
- Appendix D Ode to a galvanometer
- Appendix E The principle of the argument
- Appendix F Chase the constant
- Appendix G Are share prices in Brownian motion?
- Index
34 - Mean square convergence
from Part III - Orthogonal Series
Published online by Cambridge University Press: 19 May 2022
Foreword by
Book contents
- Frontmatter
- Epigraph
- Contents
- Foreword
- Preface
- Part I Fourier Series
- Part II Some Differential Equations
- Part III Orthogonal Series
- 32 Mean square approximation I
- 33 Mean square approximation II
- 34 Mean square convergence
- 35 The isoperimetric problem I
- 36 The isoperimetric problem II
- 37 The Sturm—Liouville equation I
- 38 Liouville
- 39 The Sturm—Liouville equation II
- 40 Orthogonal polynomials
- 41 Gaussian quadrature
- 42 Linkages
- 43 Tchebychev and uniform approximation I
- 44 The existence of the best approximation
- 45 Tchebychev and uniform approximation II
- Part IV Fourier Transforms
- Part V Further Developments
- Part VI Other Directions
- Appendix A The circle T
- Appendix B Continuous function on closed bounded sets
- Appendix C Weakening hypotheses
- Appendix D Ode to a galvanometer
- Appendix E The principle of the argument
- Appendix F Chase the constant
- Appendix G Are share prices in Brownian motion?
- Index
- Type
- Chapter
- Information
- Fourier Analysis , pp. 155 - 158Publisher: Cambridge University PressPrint publication year: 2022