Abstract

This paper addresses the issue of whether integrals of real-analytic functions remain finite under small deformations. An approach based on uniform estimates for certain classes of one-dimensional integrals is introduced. It is powerful enough to recover the stability properties of real integrals in two dimensions which follow from the work of Karpushkin, as well as produce new results in higher dimensions. In dimension three, the new stability results are sharp, as shown by the well-known example of Varchenko.

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Additional Information

ISSN
1080-6377
Print ISSN
0002-9327
Pages
pp. 519-554
Launched on MUSE
1999-06-01
Open Access
No
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