Geodesic
Spectral asymptotics for generalized Schrödinger operators
Tan Duc Do1 ; Le Xuan Truong1
1 University of Economics Ho Chi Minh City
Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 703-727.

Voir la notice de l'article provenant de la source Journal.fi

Let $d \in \{3,4,5,\ldots\}$. Consider $L = -\frac{1}{w} \, \operatorname{div}(A \, \nabla u) + \mu$ over its maximal domain in $L^2_w(\mathbb{R}^d)$. Under certain conditions on the weight $w$, the coefficient matrix $A$ and the positive Radon measure $\mu$ we obtain upper and lower bounds on $N(\lambda,L)$–the number of eigenvalues of $L$ that are at most $\lambda \ge 1$. Furthermore we show that the eigenfunctions of $L$ corresponding to those eigenvalues are exponentially decaying. In the course of proofs, we develop generalized Poincaré and weighted Young convolution inequalities as the main tools for the analysis.
DOI : 10.54330/afm.140863
Keywords: Generalized Schrödinger operator, generalized Poincaré inequality, weighted Young convolution inequality, eigenvalue asymptotic, exponential decay

Tan Duc Do 1 ; Le Xuan Truong 1

1 University of Economics Ho Chi Minh City 
@article{AFM_2023_48_2_a11,
     author = {Tan Duc Do and Le Xuan Truong},
     title = {Spectral asymptotics for generalized {Schr\"odinger} operators},
     journal = {Annales Fennici Mathematici},
     pages = {703--727},
     publisher = {mathdoc},
     volume = {48},
     number = {2},
     year = {2023},
     doi = {10.54330/afm.140863},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.54330/afm.140863/}
}
TY  - JOUR
AU  - Tan Duc Do
AU  - Le Xuan Truong
TI  - Spectral asymptotics for generalized Schrödinger operators
JO  - Annales Fennici Mathematici
PY  - 2023
SP  - 703
EP  - 727
VL  - 48
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.54330/afm.140863/
DO  - 10.54330/afm.140863
LA  - en
ID  - AFM_2023_48_2_a11
ER  - 
%0 Journal Article
%A Tan Duc Do
%A Le Xuan Truong
%T Spectral asymptotics for generalized Schrödinger operators
%J Annales Fennici Mathematici
%D 2023
%P 703-727
%V 48
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.54330/afm.140863/
%R 10.54330/afm.140863
%G en
%F AFM_2023_48_2_a11
Tan Duc Do; Le Xuan Truong. Spectral asymptotics for generalized Schrödinger operators. Annales Fennici Mathematici, Tome 48 (2023) no. 2, pp. 703-727. doi : 10.54330/afm.140863. http://geodesic.mathdoc.fr/articles/10.54330/afm.140863/

Cité par Sources :