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On the growth and stability of real-analytic functions
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 121, Number 3, June 1999
- pp. 519-554
- 10.1353/ajm.1999.0023
- Article
- Additional Information
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.