Lectures on Hermite and Laguerre Expansions. (MN-42) Book

	Preface
	Acknowledgements
Ch. 1	Hermite, Special Hermite and Laguerre Functions
1.1	Hermite and Laguerre Functions	1
1.2	Heisenberg Group and Weyl Transform	9
1.3	Special Hermite Functions	14
1.4	Hermite and Laguerre Functions on the Heisenberg Group	22
1.5	Asymptotic Properties of Hermite and Laguerre Functions	26
Ch. 2	Special Hermite Expansions
2.1	Special Hermite Expansions	29
2.2	Oscillatory Singular Integrals and Riesz Transforms	32
2.3	Littlewood-Paley-Stein Theory	39
2.4	Multipliers for Special Hermite Expansions	45
2.5	Riesz Means for Special Hermite Expansions	51
2.6	Proof of the Restriction Theorem	59
Ch. 3	Multiple Hermite Expansions
3.1	Riesz Means and the Critical Index	65
3.2	An L[superscript 2] for the Riesz Kernel	69
3.3	Almost Everywhere and Mean Summability	77
3.4	Hermite Expansions for Radial Functions	81
Ch. 4	Multipliers for Hermite Expansions
4.1	Littlewood-Paley-Stein Theory for the Hermite Semigroup	85
4.2	Marcinkiewicz Multiplier Theorem	90
4.3	Conjugate Poisson Integrals and Riesz Transforms	94
4.4	Wave Equation for the Hermite Operator	105
Ch. 5	Hermite Expansions on R
5.1	Cesaro Means and the Critical Index	111
5.2	An Expression for the Cesaro Kernel and the Basic Estimates	114
5.3	Estimating the Oscillatory Integrals	119
5.4	Almost Everywhere and Mean Summability Results	131
Ch. 6	Laguerre Expansions
6.1	The Laguerre Convolution	137
6.2	Laguerre Expansions of Convolution Type	143
6.3	Standard Laguerre Expansions	150
6.4	Laguerre Expansions of Hermite Type	156
Ch. 7	The Transplantation Theorems
7.1	The Transplantation Operators	167
7.2	Further Reduction in the Proof of the Propositions	171
7.3	Some Preliminary Lemmas	176
7.4	Estimating [actual symbol not reproducible]	181
7.5	Estimating [actual symbol not reproducible]	186
	Bibliography	193