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In frared and ultraviolet divergences of the coefficient functions of Feynman diagrams as tempered distributions. II
Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 2, pp. 199-212 Cet article a éte moissonné depuis la source Math-Net.Ru

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The results of the author are generalized to the case of nonsealar Feynman diagrams. It is shown that the analytically regularized coefficient function $F_\Gamma(\underline q)$ associated with an arbitrary graph $\Gamma$ is a functional in $S'(R^{4k})$ and an analytic function of the regularizing parameters $\lambda_l$ in some nonempty domain, from which it can be continued to the whole of $C^L$ as a meromorphic function with two series of poles (infrared and ultraviolet). Conditions under which the coefficient functions have no infrared divergences as functionals in $S'$ are obtained. It is shown how and under what conditions a coefficient function can be defined as a functional on a subspace of $S(R^{4k})$. 
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     author = {V. A. Smirnov},
     title = {In frared and ultraviolet divergences of the coefficient functions of {Feynman} diagrams as tempered {distributions.~II}},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
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     volume = {46},
     number = {2},
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V. A. Smirnov. In frared and ultraviolet divergences of the coefficient functions of Feynman diagrams as tempered distributions. II. Teoretičeskaâ i matematičeskaâ fizika, Tome 46 (1981) no. 2, pp. 199-212. http://geodesic.mathdoc.fr/item/TMF_1981_46_2_a4/

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