Abstract:
An associative algebra of generalized functions including the δ function and also functionals of a new type which are nonzero on the δ 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.
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
\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://mathscinet.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{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1981MN84000003}
Linking options:
https://www.mathnet.ru/eng/tmf2334
https://www.mathnet.ru/eng/tmf/v46/i3/p305
This publication is cited in the following 3 articles:
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
G. K. Tolokonnikov, “Shirokov algebras. I”, Theoret. and Math. Phys., 51:3 (1982), 554–561
G. K. Tolokonnikov, “Differential rings used in Shirokov algebras”, Theoret. and Math. Phys., 53:1 (1982), 952–954
Citation in format AMSBIB
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