Geodesic
Associative algebra of functionals containing $\delta(x)$ and~$r^n$
Teoretičeskaâ i matematičeskaâ fizika, Tome 52 (1982) no. 2, pp. 327-331

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

Shirokov's results [1, 2] are generalized to the case of arbitrary dimension. This leads to the construction of an associative algebra with differentiation containing the elements $\delta(\mathbf x)$ and $r^n$ ($\mathbf x=(x_1,\dots,x_d)$, $r=|\mathbf x|$, $n=0,\pm1,\pm2,\dots$). The algebra is realized on a subset of functionals defined on the space of functions which can be represented in the form $\varphi=r^{-2n_1}\varphi_1+r^{-2n_2{-1}}\varphi_2$, $\varphi_{1,2}\in S(\mathrm R^d)$. 
@article{TMF_1982_52_2_a17,
     author = {V. A. Smirnov},
     title = {Associative algebra of functionals containing $\delta(x)$ and~$r^n$},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {327--331},
     publisher = {mathdoc},
     volume = {52},
     number = {2},
     year = {1982},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1982_52_2_a17/}
}
TY  - JOUR
AU  - V. A. Smirnov
TI  - Associative algebra of functionals containing $\delta(x)$ and~$r^n$
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1982
SP  - 327
EP  - 331
VL  - 52
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_1982_52_2_a17/
LA  - ru
ID  - TMF_1982_52_2_a17
ER  - 
%0 Journal Article
%A V. A. Smirnov
%T Associative algebra of functionals containing $\delta(x)$ and~$r^n$
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1982
%P 327-331
%V 52
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_1982_52_2_a17/
%G ru
%F TMF_1982_52_2_a17
V. A. Smirnov. Associative algebra of functionals containing $\delta(x)$ and~$r^n$. Teoretičeskaâ i matematičeskaâ fizika, Tome 52 (1982) no. 2, pp. 327-331. http://geodesic.mathdoc.fr/item/TMF_1982_52_2_a17/