RT Dissertation/Thesis
T1 Dunkl harmonic oscillator and Witten's perturbation on strata
A1 Calaza Cabanas, Manuel
K1 Dunkl harmonic oscillator
K1 Witten's perturbation method
AB The main goal of this work is to use Witten's perturbation method to prove aversion of Morse inequalities for the minimum and maximum ideal boundary conditionsof the de Rham complex on strata, endowed with adapted metrics, wherecompact Thom-Mather strati cations are considered. For that purpose, we study rst eigenfunction estimates and embedding results for the Dunkl harmonic oscillatoron the line, which are generalized to other related operators on R+. Thestudy of these operators is the key ingredient in our local analysis of the Witten'sperturbation.Thus this thesis has two main parts. The  rst part is devoted to the study ofeigenfunction estimates and embedding results for the Dunkl harmonic oscillatorand related operators. The second part deals with the Witten's perturbation onstrata, where the  rst part is used.This work is published in the preprints [1, 2].Let us introduce those chapters separately and state their main results.
YR 2012
FD 2012-09-19
LK http://hdl.handle.net/10347/6103
UL http://hdl.handle.net/10347/6103
LA eng
DS Minerva
RD 23 abr 2026