.png){kind=icon}
.png){kind=icon}
Return
SHARP LOCAL Lp ESTIMATES FOR THE HERMITE EIGENFUNCTIONS
.png){kind=icon}
PRE
AI
DOI：10.1090/tran/9465.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
We investigate the concentration of eigenfunctions for the Hermite operator H = -Delta + |x |(2) in Rn by establishing local L-p bounds over the compact sets with arbitrary dilations and translations. These results extend the local estimates by Thangavelu [Duke Math. J. 94 (1998), pp. 257-278] and Koch-Tataru [Duke Math. J. 128 (2005), pp. 369-392], and explain the special phenomenon that the global L-p bounds decrease in p when 2 < p < (2n+6 )/(n+1) The key L-2-estimates show that the local probabilities decrease away from the boundary { |x | =lambda }, and then they satisfy Bohr's correspondence principle in any dimension. The proof uses the Hermite spectral projection operator represented by Mehler's formula for the Hermite-Schrodinger propagator e(-itH) , and the strategy developed by Thangavelu [Duke Math. J. 94 (1998), pp. 257-278] and Jeong-Lee-Ryu [Hermite spectral projection operator]. We also exploit an explicit version of the stationary phase lemma and Hormander's L-2 oscillatory integral theorem. Using Koch-Tataru's strategy, we construct appropriate examples to illustrate the possible concentrations and show the optimality of our local estimates.
Keywords:
KAKEYA-NIKODYM BOUNDS
NODAL SETS
OSCILLATORY INTEGRALS
CARLEMAN INEQUALITIES
TORAL EIGENFUNCTIONS
RIEMANNIAN SURFACES
HARMONIC-OSCILLATOR
QUANTUM ERGODICITY
RESTRICTION
OPERATORS
Journal
T
IF:
1.2
Papers:
180
Citations:
0