## 2 Citations

### Bounds on the Hermite spectral projection operator

- Mathematics
- 2022

. We study L p – L q bounds on the spectral projection operator Π λ associated to the Hermite operator H = | x | 2 − ∆ in R d . We are mainly con- cerned with a localized operator χ E Π λ χ E for a…

### Endpoint eigenfunction bounds for the Hermite operator

- Mathematics
- 2022

. We establish the optimal L p , p = 2( d + 3) / ( d + 1) , eigenfunction bound for the Hermite operator H = − ∆ + | x | 2 on R d . Let Π λ denote the projection operator to the vector space spanned…

## References

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### Lectures on Hermite and Laguerre expansions

- Mathematics
- 1993

The interplay between analysis on Lie groups and the theory of special functions is well known. This monograph deals with the case of the Heisenberg group and the related expansions in terms of…

### BMO results for operators associated to Hermite expansions

- Mathematics
- 2005

We prove BMO and L∞ results for operators associated to the heat-diffusion and Poisson semigroups in the multi-dimensional Hermite function expansions setting. These include maximal functions and…

### On the multilinear restriction and Kakeya conjectures

- Mathematics
- 2005

We prove d-linear analogues of the classical restriction and Kakeya conjectures in Rd. Our approach involves obtaining monotonicity formulae pertaining to a certain evolution of families of…

### SUMMABILITY OF HERMITE EXPANSIONS

- Mathematics, Philosophy
- 2010

We study the summability of one-dimensional Hermite expansions. We prove that the critical index for the Riesz summability is 1 /6 . We also prove analogues of the Fejer-Lebesgue theorem and…

### L^p eigenfunction bounds for the Hermite operator

- Mathematics
- 2004

Author(s): Koch, Herbert; Tataru, Daniel | Abstract: We obtain L^p eigenfunction bounds for the harmonic oscillator in R^n and for other related operators, improving earlier results of Thangavelu and…

### Improved bounds for Bochner-Riesz and maximal Bochner-Riesz operators

- Mathematics
- 2004

In this note we improve the known L p-bounds for Bochner-Riesz operators and their maximal operators.

### On the boundary convergence of solutions to the Hermite-Schr\

- Mathematics
- 2009

In the half-space $\mathbb{R}^d \times \mathbb{R}_+$, we consider the Hermite-Schrodinger equation $i\partial u/\partial t = - \Delta u + |x|^2 u$, with given boundary values on $\mathbb{R}^d$.
We…