Abstract
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 where the submanifold is a complex hypersurface in a complex manifold and where it is a boundary component of a manifold with boundary, arising in string perturbation theory, are treated in more detail.
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Felder, G., Kazhdan, D.: Divergent Integrals, Residues of Dolbeault Forms, and Asymptotic Riemann Mappings. arXiv:1602.02738 [math.CV]. Int. Math. Res. Not. First published online. doi:10.1093/imrn/rnw190
Gelfand, I.M., Shilov, G.E.: Generalized Functions, vol. 1. Properties and Operations, translated from the 1958 Russian original by Saletan, E. AMS Chelsea Publishing, Providence, RI (2016)
Hadamard, J.: Lectures on Cauchy’s Problem in Linear Partial Differential Equations. Dover Publications, New York (1953). Originally published by Yale University Press (1923)
Itzykson, C., Zuber, J.-B.: Quantum Field Theory. McGraw-Hill International Book Co., New York (1980)
Witten, E.: String Perturbation Theory. Revisited. arXiv:1209.5461 [hep-th]
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Dedicated to Sasha Beilinson the occasion of his 60th birthday.
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Felder, G., Kazhdan, D. Regularization of divergent integrals. Sel. Math. New Ser. 24, 157–186 (2018). https://doi.org/10.1007/s00029-017-0323-9
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DOI: https://doi.org/10.1007/s00029-017-0323-9