Associative algebra of generalized functions closed with respect to differentiation and integration
Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 3, pp. 305-309
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An associative algebra of generalized functions including the $\delta$ function and also functionals of a new type which are nonzero on the $\delta$ function and its derivatives is constructed. Involution, differentiation, and integration are defined in the algebra. It can be used to construct new strongly singular potentials and also in the Hamiltonian formulation of local quantum field theory.
@article{TMF_1981_46_3_a2,
author = {G. K. Tolokonnikov and Yu. M. Shirokov},
title = {Associative algebra of generalized functions closed with respect to differentiation and integration},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {305--309},
publisher = {mathdoc},
volume = {46},
number = {3},
year = {1981},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_1981_46_3_a2/}
}
TY - JOUR AU - G. K. Tolokonnikov AU - Yu. M. Shirokov TI - Associative algebra of generalized functions closed with respect to differentiation and integration JO - Teoretičeskaâ i matematičeskaâ fizika PY - 1981 SP - 305 EP - 309 VL - 46 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_1981_46_3_a2/ LA - ru ID - TMF_1981_46_3_a2 ER -
%0 Journal Article %A G. K. Tolokonnikov %A Yu. M. Shirokov %T Associative algebra of generalized functions closed with respect to differentiation and integration %J Teoretičeskaâ i matematičeskaâ fizika %D 1981 %P 305-309 %V 46 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_1981_46_3_a2/ %G ru %F TMF_1981_46_3_a2
G. K. Tolokonnikov; Yu. M. Shirokov. Associative algebra of generalized functions closed with respect to differentiation and integration. Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 3, pp. 305-309. http://geodesic.mathdoc.fr/item/TMF_1981_46_3_a2/