Book contents
- Frontmatter
- Contents
- Preface
- What's good about this book?
- Suggested 12-week syllabus
- Part I Motivating examples and major applications
- Part II General theory
- Part III Fourier series on bounded domains
- 6 Some functional analysis
- 7 Fourier sine series and cosine series
- 8 Real Fourier series and complex Fourier series
- 9 Multidimensional Fourier series
- 10 Proofs of the Fourier convergence theorems
- Part IV BVP solutions via eigenfunction expansions
- Part V Miscellaneous solution methods
- Part VI Fourier transforms on unbounded domains
- Appendix A Sets and functions
- Appendix B Derivatives – notation
- Appendix C Complex numbers
- Appendix D Coordinate systems and domains
- Appendix E Vector calculus
- Appendix F Differentiation of function series
- Appendix G Differentiation of integrals
- Appendix H Taylor polynomials
- References
- Subject index
- Notation index
10 - Proofs of the Fourier convergence theorems
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface
- What's good about this book?
- Suggested 12-week syllabus
- Part I Motivating examples and major applications
- Part II General theory
- Part III Fourier series on bounded domains
- 6 Some functional analysis
- 7 Fourier sine series and cosine series
- 8 Real Fourier series and complex Fourier series
- 9 Multidimensional Fourier series
- 10 Proofs of the Fourier convergence theorems
- Part IV BVP solutions via eigenfunction expansions
- Part V Miscellaneous solution methods
- Part VI Fourier transforms on unbounded domains
- Appendix A Sets and functions
- Appendix B Derivatives – notation
- Appendix C Complex numbers
- Appendix D Coordinate systems and domains
- Appendix E Vector calculus
- Appendix F Differentiation of function series
- Appendix G Differentiation of integrals
- Appendix H Taylor polynomials
- References
- Subject index
- Notation index
Summary
- Type
- Chapter
- Information
- Linear Partial Differential Equations and Fourier Theory , pp. 197 - 226Publisher: Cambridge University PressPrint publication year: 2010