Geodesic
Convergence of regularized traces of powers of the~Laplace--Beltrami operator with potential on the sphere~$S^n$
Sbornik. Mathematics, Tome 190 (1999) no. 10, pp. 1401-1415

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

For the Laplace–Beltrami operator $-\Delta$ on the sphere $S^n$ perturbed by the operator of multiplication by an infinitely smooth complex-valued function $q$, the convergence without brackets of regularized traces $$ \sum_k\biggl(\mu_k^\alpha -\lambda_k^\alpha-\sum_j\chi_j(\alpha )\lambda_k^{k_j(\alpha)}\biggr), $$ is studied, where the $\mu_k$ and the $\lambda_k$ are the eigenvalues of the operators $-\Delta+q$ and $-\Delta$, respectively. Sharp estimates of $\alpha$ in the cases of absolute and conditional convergence are obtained. Explicit formulae for the coefficients $\chi_j$ are obtained for odd potentials $q$. 
@article{SM_1999_190_10_a0,
     author = {A. N. Bobrov and V. E. Podolskii},
     title = {Convergence of regularized traces of powers of {the~Laplace--Beltrami} operator with potential on the sphere~$S^n$},
     journal = {Sbornik. Mathematics},
     pages = {1401--1415},
     publisher = {mathdoc},
     volume = {190},
     number = {10},
     year = {1999},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1999_190_10_a0/}
}
TY  - JOUR
AU  - A. N. Bobrov
AU  - V. E. Podolskii
TI  - Convergence of regularized traces of powers of the~Laplace--Beltrami operator with potential on the sphere~$S^n$
JO  - Sbornik. Mathematics
PY  - 1999
SP  - 1401
EP  - 1415
VL  - 190
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1999_190_10_a0/
LA  - en
ID  - SM_1999_190_10_a0
ER  - 
%0 Journal Article
%A A. N. Bobrov
%A V. E. Podolskii
%T Convergence of regularized traces of powers of the~Laplace--Beltrami operator with potential on the sphere~$S^n$
%J Sbornik. Mathematics
%D 1999
%P 1401-1415
%V 190
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1999_190_10_a0/
%G en
%F SM_1999_190_10_a0
A. N. Bobrov; V. E. Podolskii. Convergence of regularized traces of powers of the~Laplace--Beltrami operator with potential on the sphere~$S^n$. Sbornik. Mathematics, Tome 190 (1999) no. 10, pp. 1401-1415. http://geodesic.mathdoc.fr/item/SM_1999_190_10_a0/