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Lectures on Hermite and Laguerre expansions /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, N.J. :
Princeton University Press,
1993.
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| Colección: | Mathematical notes (Princeton University Press) ;
42. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Ch. 1. Hermite, Special Hermite and Laguerre Functions. 1.1. Hermite and Laguerre Functions. 1.2. Heisenberg Group and Weyl Transform. 1.3. Special Hermite Functions. 1.4. Hermite and Laguerre Functions on the Heisenberg Group. 1.5. Asymptotic Properties of Hermite and Laguerre Functions
- Ch. 2. Special Hermite Expansions. 2.1. Special Hermite Expansions. 2.2. Oscillatory Singular Integrals and Riesz Transforms. 2.3. Littlewood-Paley-Stein Theory. 2.4. Multipliers for Special Hermite Expansions. 2.5. Riesz Means for Special Hermite Expansions. 2.6. Proof of the Restriction Theorem
- Ch. 3. Multiple Hermite Expansions. 3.1. Riesz Means and the Critical Index. 3.2. An L[superscript 2] for the Riesz Kernel. 3.3. Almost Everywhere and Mean Summability. 3.4. Hermite Expansions for Radial Functions
- Ch. 4. Multipliers for Hermite Expansions. 4.1. Littlewood-Paley-Stein Theory for the Hermite Semigroup. 4.2. Marcinkiewicz Multiplier Theorem. 4.3. Conjugate Poisson Integrals and Riesz Transforms.
- 4.4. Wave Equation for the Hermite Operator
- Ch. 5. Hermite Expansions on R. 5.1. Cesaro Means and the Critical Index. 5.2. An Expression for the Cesaro Kernel and the Basic Estimates. 5.3. Estimating the Oscillatory Integrals. 5.4. Almost Everywhere and Mean Summability Results
- Ch. 6. Laguerre Expansions. 6.1. The Laguerre Convolution. 6.2. Laguerre Expansions of Convolution Type. 6.3. Standard Laguerre Expansions. 6.4. Laguerre Expansions of Hermite Type
- Ch. 7. The Transplantation Theorems. 7.1. The Transplantation Operators. 7.2. Further Reduction in the Proof of the Propositions. 7.3. Some Preliminary Lemmas. 7.4. Estimating [actual symbol not reproducible]. 7.5. Estimating [actual symbol not reproducible].