Fundamentals of Fourier Analysis
This self-contained text introduces Euclidean Fourier Analysis to graduate students who have completed courses in Real Analysis and Complex Variables. It provides sufficient content for a two course sequence in Fourier Analysis or Harmonic Analysis at the graduate level. In true pedagogical spirit,...
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| Главный автор: | |
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| Соавтор: | |
| Формат: | Электронный ресурс eКнига |
| Язык: | английский |
| Опубликовано: |
Cham :
Springer International Publishing : Imprint: Springer,
2024.
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| Редактирование: | 1st ed. 2024. |
| Серии: | Graduate Texts in Mathematics,
302 |
| Предметы: | |
| Online-ссылка: | https://doi.org/10.1007/978-3-031-56500-7 |
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Оглавление:
- 1 Introductory Material
- 2 Fourier Transforms, Tempered Distributions, Approximate Identities
- 3 Singular Integrals
- 4 Vector-Valued Singular Integrals and Littlewood–Paley Theory
- 5 Fractional Integrability or Differentiability and Multiplier Theorems
- 6 Bounded Mean Oscillation
- 7 Hardy Spaces
- 8 Weighted Inequalities
- Historical Notes
- Appendix A Orthogonal Matrices
- Appendix B Subharmonic Functions
- Appendix C Poisson Kernel on the Unit Strip
- Appendix D Density for Subadditive Operators
- Appendix E Transposes and Adjoints of Linear Operators
- Appendix F Faa di Bruno Formula
- Appendix G Besicovitch Covering Lemma
- Glossary
- References
- Index.