Commutative harmonic analysis II group methods in commutative harmonic analysis
| Otros Autores: | , |
|---|---|
| Formato: | Libro |
| Idioma: | Inglés |
| Publicado: |
Berlin ; Barcelona :
Springer
cop. 1998.
|
| Colección: | Encyclopaedia of mathematical sciences ;
25. |
| Materias: | |
| Ver en Universidad de Navarra: | https://unika.unav.edu/discovery/fulldisplay?docid=alma991007027509708016&context=L&vid=34UNAV_INST:VU1&search_scope=34UNAV_TODO&tab=34UNAV_TODO&lang=es |
Tabla de Contenidos:
- Ch. 1. Convolution and Translation in Classical Analysis. 1. Introduction. 2. The Fourier Transform in L[superscript 1](R[superscript n]). 3. The Plancherel Theorem. 4. Eigenfunctions of the Fourier Transform. 5. Integral Transforms in Harmonic Analysis. 6. Translation-invariant Subspaces in L[superscript 2](R). 7. A Generalization of the Fourier-Plancherel and Paley-Wiener Theorems and M.G. Krein's String Theory. 8. Positive Definite Functions. 9. Positive Definite Kernels and the Problem of Extending Positive Definite Functions. 10. Negative Definite Functions and the Arithmetic of Probability Measures. 11. Wiener's Tauberian Theorem. 12. Introduction to the Spectral Theory of Bounded and Increasing Functions on R
- Ch. 2. Invariant Integration and Harmonic Analysis on Locally Compact Abelian Groups. 1. Introduction. 2. Topological Groups (Basic Definitions and Facts). 3. Special Locally Compact Abelian Groups. Locally Compact Rings and Fields. Examples.
- 4. Integration on Locally Compact Hausdorff Spaces. 5. The Haar Measure and the Haar Integral. 6. Invariant Means on Topological Groups. 7. Commutative Banach Algebras. 8. Elements of Harmonic Analysis on Locally Compact Abelian Groups. 9. Duality Properties and Poisson's Formula. 10. General and Special Structural Theorems.
