Book contents
- Frontmatter
- Epigraph
- Contents
- Foreword
- Preface
- Part I Fourier Series
- 1 Introduction
- 2 Proof of Fejér’s theorem
- 3 Weyl’s equidistribution theorem
- 4 The Weierstrass polynomial approximation theorem
- 5 A second proof of Weierstrass’s theorem
- 6 Hausdorff’s moment problem
- 7 The importance of linearity
- 8 Compass and tides
- 9 The simplest convergence theorem
- 10 The rate of convergence
- 11 A nowhere differentiable function
- 12 Reactions
- 13 Monte Carlo methods
- 14 Mathematical Brownian motion
- 15 Pointwise convergence
- 16 Behaviour at points of discontinuity I
- 17 Behaviour at points of discontinuity II
- 18 A Fourier series divergent at a point
- 19 Pointwise convergence, the answer
- Part II Some Differential Equations
- Part III Orthogonal Series
- 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
16 - Behaviour at points of discontinuity I
from Part I - Fourier Series
Published online by Cambridge University Press: 19 May 2022
Foreword by
Book contents
- Frontmatter
- Epigraph
- Contents
- Foreword
- Preface
- Part I Fourier Series
- 1 Introduction
- 2 Proof of Fejér’s theorem
- 3 Weyl’s equidistribution theorem
- 4 The Weierstrass polynomial approximation theorem
- 5 A second proof of Weierstrass’s theorem
- 6 Hausdorff’s moment problem
- 7 The importance of linearity
- 8 Compass and tides
- 9 The simplest convergence theorem
- 10 The rate of convergence
- 11 A nowhere differentiable function
- 12 Reactions
- 13 Monte Carlo methods
- 14 Mathematical Brownian motion
- 15 Pointwise convergence
- 16 Behaviour at points of discontinuity I
- 17 Behaviour at points of discontinuity II
- 18 A Fourier series divergent at a point
- 19 Pointwise convergence, the answer
- Part II Some Differential Equations
- Part III Orthogonal Series
- 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. 59 - 61Publisher: Cambridge University PressPrint publication year: 2022