Hostname: page-component-7dd5485656-g8tfn Total loading time: 0 Render date: 2025-10-31T13:52:09.393Z Has data issue: false hasContentIssue false
  • English
  • Français

Residue Integrals and their Mellin Transforms

Published online by Cambridge University Press:  20 November 2018

Mikael Passare  and
August Tsikh
Mikael Passare
Affiliation:
Matematiska institutionen, Stockholms universitet, 10691 Stockholm, Sweden
August Tsikh
Affiliation:
Krasnoyarskiĭ gosudarstvennyĭ universitet, Prospekt Svobodnyĭ 79, 660 062 Krasnoyarsk, Russia
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Given an almost arbitrary holomorphic map we study the structure of the associated residue integral and its Mellin transform, and the relation between these two objects. More precisely, we relate the limit behaviour of the residue integral to the polar structure of the Mellin transform. We consider also ideals connected to nonisolated singularities.

Keywords

32A2732H0213J0744A30

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 5 , 01 October 1995 , pp. 1037 - 1050
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Berenstein, C.A., Gay, R., Vidras, A. and Yger, A., Residue currents and Bézout identities, Progress in Math. 114, Birkhäuser Verlag, Basel, 1993.Google Scholar
2. Coleffand, N. Herrera, M., Les courants résiduels associés à une forme méromorphe, Lecture Notes in Math. 633, Berlin, 1978.Google Scholar
3. Griffiths, P. and Harris, J., Principles of algebraic geometry, Pure and Applied Math., John Wiley and Sons, New York, 1978.Google Scholar
4. Hironaka, H., The resolution of singularities of an algebraic variety over afield of characteristic zero, Ann. of Math. 79(1964), 109–326.Google Scholar
5. Palamodov, V., On the multiplicity of a holomorphic map (Russian), Funktsional. Anal, i Prilozhen. 1: 3(1967), 54–65.Google Scholar
6. Passare, M.,v4 calculus for meromorphic currents, J. Reine Angew. Math. 392(1988), 37–56.Google Scholar
7. Solomin, J., Le résidu logarithmique dans les intersections non complètes, C.R. Acad. Sci. Paris 284(1977), 1061–1064.Google Scholar
8. Tsikh, A., On the multiplicities of a holomorphic mapping at non-isolated zeros, and the Milnor numbers of a one-dimensional singularity (Russian). In: Komleksnyj analiz i matematičeskaja fizika, Physics Institute, Krasnoyarsk, 1988. 113–124.Google Scholar
9. Tsikh, A., Multidimensional residues and their applications, Transi. Math. Monographs 103, Amer. Math. Soc, Providence, 1992.Google Scholar