Ducomet, B. Logarithmic asymptotic behaviour of the renormalized G-convolution product in four-dimensional Euclidean space. (English) Zbl 0557.46043 Ann. Inst. Henri Poincaré, Phys. Théor. 41, 1-24 (1984). We give an asymptotic logarithmic behaviour in r-dimensional Euclidean momentum space, of the renormalized G-convolution product \(H_ G^{ren}\) associated with a generalized graph G. this convolution product was introduced and studied in a regularized context by J. Bros and M. Lassalle in axiomatic quantum field theory. The present work is an extension of previous results of M. Manolessou, which contained only the power asymptotic behaviour with respect to external momenta. Cited in 1 Document MSC: 46N99 Miscellaneous applications of functional analysis 81T17 Renormalization group methods applied to problems in quantum field theory 46F10 Operations with distributions and generalized functions Keywords:asymptotic logarithmic behaviour; renormalized G-convolution product PDFBibTeX XMLCite \textit{B. Ducomet}, Ann. Inst. Henri Poincaré, Phys. Théor. 41, 1--24 (1984; Zbl 0557.46043) Full Text: Numdam EuDML References: [1] J. Bros , M. Manolessou-Grammaticou , Commun. Math. Phys. , t. 72 , 1980 , p. 175 - 205 ; Commun. Math. Phys. , t. 72 , 1980 , p. 207 - 237 . [2] M. Manolessou-Grammaticou , Thesis , Orsay , 1977 . [3] M. Manolessou-Grammaticou , Ann. Phys. , t. 122 , 1979 , p. 297 - 320 . MR 551238 [4] M. Manolessou-Grammaticou , Renormalized normal product and equations of motion of \Phi 4-coupling . Preprint Bielefeld ( 1982 ). Private communications. MR 738678 [5] S. Weinberg , Phys. Rev. , t. 118 , 1960 , p. 838 - 849 . MR 116953 | Zbl 0098.20403 · Zbl 0098.20403 · doi:10.1103/PhysRev.118.838 [6] J.P. Fink , J. Math. Phys. , t. 9 , 1968 , p. 1389 - 1400 . MR 234692 | Zbl 0159.60003 · Zbl 0159.60003 · doi:10.1063/1.1664727 [7] B. Ducomet , Taylor rests of graded Weinberg functions (C. E. A. Technical Report). This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.