Geodesic
On the Structure of the Bochner--Martinelli Residue Currents
Informatics and Automation, Complex analysis and its applications, Tome 298 (2017), pp. 7-19.

Voir la notice de l'article provenant de la source Math-Net.Ru

We study residue currents of the Bochner–Martinelli type using their relationship to the Mellin transforms of residue integrals. We present a structure formula for residue currents associated with dimension-reducing monomial mappings: they can be represented as sums of products of simple residue currents, principal value currents, and hypergeometric functions.
Keywords: residue current, Bochner–Martinelli kernel, Mellin transform.
Mots-clés : principal value current, Leray residue form 
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I. A. Antipova. On the Structure of the Bochner--Martinelli Residue Currents. Informatics and Automation, Complex analysis and its applications, Tome 298 (2017), pp. 7-19. http://geodesic.mathdoc.fr/item/TRSPY_2017_298_a0/

[1] Aizenberg L. A., Yuzhakov A. P., Integralnye predstavleniya i vychety v mnogomernom kompleksnom analize, Nauka, Novosibirsk, 1979 | MR

[2] Andersson M., “Residue currents and ideals of holomorphic functions”, Bull. sci. math., 128:6 (2004), 481–512 | DOI | MR | Zbl

[3] Antipova I. A., “Obrascheniya mnogomernykh preobrazovanii Mellina i resheniya algebraicheskikh uravnenii”, Mat. sb., 198:4 (2007), 3–20 | DOI | MR | Zbl

[4] Berenstein C. A., Gay R., Yger A., “Analytic continuation of currents and division problems”, Forum math., 1 (1989), 15–51 | DOI | MR | Zbl

[5] Berenstein C. A., Yger A., “Analytic residue theory in the non-complete intersection case”, J. reine angew. Math., 527 (2000), 203–235 | MR | Zbl

[6] Coleff N. R., Herrera M. E., Les courants résiduels associés à une forme méromorphe, Lect. Notes Math., 633, Springer, Berlin, 1978 | DOI | MR

[7] Dolbeault P., About the characterization of some residue currents, 2010, arXiv: 1002.3025 [math.CV] | MR

[8] Flajolet P., Gourdon X., Dumas P., “Mellin transforms and asymptotics: Harmonic sums”, Theor. Comput. Sci., 144 (1995), 3–58 | DOI | MR | Zbl

[9] Passare M., “Residues, currents, and their relation to ideals of holomorphic functions”, Math. Scand., 62:1 (1988), 75–152 | DOI | MR | Zbl

[10] Passare M., Tsikh A., “Residue integrals and their Mellin transforms”, Can. J. Math., 47:5 (1995), 1037–1050 | DOI | MR | Zbl

[11] Passare M., Tsikh A., Yger A., “Residue currents of the Bochner–Martinelli type”, Publ. Mat., 44:1 (2000), 85–117 | DOI | MR | Zbl

[12] Samuelsson H., “Regularizations of products of residue and principal value currents”, J. Funct. Anal., 239:2 (2006), 566–593 | DOI | MR | Zbl

[13] Shchuplev A., Tsikh A., Yger A., “Residual kernels with singularities on coordinate planes”, Tr. MIAN, 253, 2006, 277–295 | MR | Zbl

[14] Tsikh A. K., Mnogomernye vychety i ikh primeneniya, Nauka, Novosibirsk, 1988 | MR

[15] Tsikh A., Yger A., “Residue currents”, J. Math. Sci., 120:6 (2004), 1916–1971 | DOI | MR | Zbl

[16] Wulcan E., “Residue currents of monomial ideals”, Indiana Univ. Math. J., 56:1 (2007), 365–388 | DOI | MR | Zbl