Regularization of divergent integrals

Preprint English OPEN
Felder, Giovanni; Kazhdan, David;
(2016)
  • Subject: Mathematical Physics | Mathematics - Differential Geometry
    arxiv: Mathematics::Differential Geometry | Mathematics::Symplectic Geometry

We study the Hadamard finite part of divergent integrals of differential forms with singularities on submanifolds. We give formulae for the dependence of the finite part on the choice of regularization and express them in terms of a suitable local residue map. The cases... View more
  • References (6)

    ω = Re s ≫ 0.

    [1] Giovanni Felder and David Kazhdan, Divergent Integrals, Residues of Dolbeault Forms, and Asymptotic Riemann Mappings, arXiv:1602.02738 [math.CV], Int. Math. Res. Notices, first published online, doi:10.1093/imrn/rnw190.

    [2] I.M. Gelfand and G.E. Shilov. Generalized functions. Vol. 1. Properties and operations, translated from the 1958 Russian original by Eugene Saletan, AMS Chelsea Publishing, Providence, RI, 2016.

    [3] Jacques Hadamard, Lectures on Cauchy's problem in linear partial differential equations, Dover Publications, New York, 1953, originally published by Yale University Press in 1923.

    [4] Claude Itzykson and Jean-Bernard Zuber, Quantum field theory, McGraw-Hill International Book Co., New York, 1980.

    [5] Edward Witten, String perturbation theory revisited, arXiv:1209.5461 [hep-th]. Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem 91904, Israel E-mail address: kazhdan@math.huji.ac.il

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