Geodesic
Associative algebra of generalized functions closed with respect to differentiation and integration
Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 3, pp. 305-309 
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/
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     title = {Associative algebra of generalized functions closed with respect to differentiation and integration},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Shirokov Yu. M., “Algebra odnomernykh obobschennykh funktsii”, TMF, 39:3 (1979), 291–301 | MR | Zbl

[2] Shirokov Yu. M., “Silno singulyarnye potentsialy v odnomernoi kvantovoi mekhanike”, TMF, 41:3 (1979), 291–302 | MR | Zbl

[3] Shirokov Yu. M., “Silno singulyarnye potentsialy v trekhmernoi kvantovoi mekhanike”, TMF, 42:1 (1980), 45–49 | MR

[4] Shirokov Yu. M., “Algebra trekhmernykh obobschennykh funktsii”, TMF, 40:3 (1979), 348–354 | MR | Zbl

[5] Ivanov V. K., “Algebra, porozhdaemaya funktsiei Khevisaida i delta-funktsiyami”, Izv. vuzov, matem., 185:10 (1977), 65–69 | MR | Zbl

[6] Berg L., “Representation for Distribution Algebras”, Z. angew. Math. und Mech., B56:5 (1976), 177–181 | DOI | MR | Zbl

[7] Keller K., On the multiplication of distributions, I, Preprint Institut für theoretische Physik, Aachen, 1975