Geodesic
The renormalizing series of some integral equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 299-313 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We consider integral equations for which the perturbation expansion gives a power series in a parameter $h$ whose coefficients are divergent integrals. We eliminate the divergent integrals by introducing a renormalizing $Z(t,h)$ series in the minimal subtraction scheme. We investigate the convergence of the formal $Z$ series in relation to the kernels of the integral equations. We find a relation of the renormalizing series to the Lagrange inversion series and also some other relations.
Keywords: renormalization, divergent integral
Mots-clés : Lagrange inversion formula. 
@article{TMF_2010_163_2_a5,
     author = {B. Candelpergher and T. Grandou},
     title = {The~renormalizing series of some integral equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {299--313},
     year = {2010},
     volume = {163},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a5/}
}
TY  - JOUR
AU  - B. Candelpergher
AU  - T. Grandou
TI  - The renormalizing series of some integral equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2010
SP  - 299
EP  - 313
VL  - 163
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a5/
LA  - ru
ID  - TMF_2010_163_2_a5
ER  - 
%0 Journal Article
%A B. Candelpergher
%A T. Grandou
%T The renormalizing series of some integral equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2010
%P 299-313
%V 163
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a5/
%G ru
%F TMF_2010_163_2_a5
B. Candelpergher; T. Grandou. The renormalizing series of some integral equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 163 (2010) no. 2, pp. 299-313. http://geodesic.mathdoc.fr/item/TMF_2010_163_2_a5/

[1] D. Kreimer, Knots and Feynman Diagrams, Cambridge Lecture Notes Phys., 13, Cambridge Univ. Press, Cambridge, 2000 | MR | Zbl

[2] A. Connes, D. Kreimer, Comm. Math. Phys., 199:1 (1998), 203–242 | DOI | MR | Zbl

[3] J. C. Collins, Renormalization, Cambridge Monogr Math. Phys., Cambridge Univ. Press, Cambridge, 1984 | MR | Zbl

[4] I. Bierenbaum, R. Kreckel, D. Kreimer, J. Math. Phys., 43:10 (2002), 4721–4740 | DOI | MR | Zbl

[5] E. T. Uitteker, Dzh. N. Vatson, Kurs sovremennogo analiza, Ch. 1, 2, Nauka, M., 1963 | MR | Zbl