Geodesic
The asymptotic behavior of the spectral function for elliptic operators in an unbounded region
Matematičeskie zametki, Tome 5 (1969) no. 2, pp. 245-251 
G. I. Bass. The asymptotic behavior of the spectral function for elliptic operators in an unbounded region. Matematičeskie zametki, Tome 5 (1969) no. 2, pp. 245-251. http://geodesic.mathdoc.fr/item/MZM_1969_5_2_a11/
@article{MZM_1969_5_2_a11,
     author = {G. I. Bass},
     title = {The asymptotic behavior of the spectral function for elliptic operators in an~unbounded region},
     journal = {Matemati\v{c}eskie zametki},
     pages = {245--251},
     year = {1969},
     volume = {5},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1969_5_2_a11/}
}
TY  - JOUR
AU  - G. I. Bass
TI  - The asymptotic behavior of the spectral function for elliptic operators in an unbounded region
JO  - Matematičeskie zametki
PY  - 1969
SP  - 245
EP  - 251
VL  - 5
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MZM_1969_5_2_a11/
LA  - ru
ID  - MZM_1969_5_2_a11
ER  - 
%0 Journal Article
%A G. I. Bass
%T The asymptotic behavior of the spectral function for elliptic operators in an unbounded region
%J Matematičeskie zametki
%D 1969
%P 245-251
%V 5
%N 2
%U http://geodesic.mathdoc.fr/item/MZM_1969_5_2_a11/
%G ru
%F MZM_1969_5_2_a11

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider elliptic self-adjoint differential operators $L$ of order $2m$ in a bounded region $D\subset R_n$. An asymptotic formula for the function $N(\lambda)=\sum\limits_{\lambda_n<\lambda}1$ the number of eigenvalues of the operator $L$ less than $\lambda$ is proved: $$ N(\lambda)=M_0\lambda{n/2m}+o(\lambda^{n/2m}) $$ where $\lambda\to+\infty$ and $M_0$ is the following constant: $$ M_0=\frac{V_D}{(2\pi)^n\Gamma(1+n/2m)}\int_{R_n}e^{-L(s)}\,ds. $$