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 TMF, 1981, Volume 46, Number 3, Pages 305–309 (Mi tmf2334)

Associative algebra of generalized functions closed with respect to differentiation and integration

G. K. Tolokonnikov, Yu. M. Shirokov

Abstract: 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.

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English version:
Theoretical and Mathematical Physics, 1981, 46:3, 200–203

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Citation: G. K. Tolokonnikov, Yu. M. Shirokov, “Associative algebra of generalized functions closed with respect to differentiation and integration”, TMF, 46:3 (1981), 305–309; Theoret. and Math. Phys., 46:3 (1981), 200–203

Citation in format AMSBIB
\Bibitem{TolShi81} \by G.~K.~Tolokonnikov, Yu.~M.~Shirokov \paper Associative algebra of generalized functions closed with respect to differentiation and integration \jour TMF \yr 1981 \vol 46 \issue 3 \pages 305--309 \mathnet{http://mi.mathnet.ru/tmf2334} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=622510} \zmath{https://zbmath.org/?q=an:0464.46038|0479.46022} \transl \jour Theoret. and Math. Phys. \yr 1981 \vol 46 \issue 3 \pages 200--203 \crossref{https://doi.org/10.1007/BF01032726} \isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1981MN84000003} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. G. K. Tolokonnikov, “Shirokov algebras. I”, Theoret. and Math. Phys., 51:3 (1982), 554–561
2. G. K. Tolokonnikov, “Differential rings used in Shirokov algebras”, Theoret. and Math. Phys., 53:1 (1982), 952–954
3. V. G. Danilov, V. P. Maslov, V. M. Shelkovich, “Algebras of the singularities of singular solutions to first-order quasi-linear strictly hyperbolic systems”, Theoret. and Math. Phys., 114:1 (1998), 1–42
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