The Stationary Phase Method for Real Analytic Geometry

Authors

Domenico Napoletani, Chapman UniversityFollow
Daniele C. Struppa, Chapman UniversityFollow

Document Type

Article

Publication Date

12-30-2015

Abstract

We prove that the existence of isolated solutions of systems of equations of analytical functions on compact real domains in R^p, is equivalent to the convergence of the phase of a suitable complex valued integral I(h) for h→∞. As an application, we then use this result to prove that the problem of establishing the irrationality of the value of an analytic function F(x) at a point x₀ can be rephrased in terms of a similar phase convergence.

Comments

NOTICE: this is the author’s version of a work that was accepted for publication in Journal of Mathematical Analysis and Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Journal of Mathematical Analysis and Applications in 2015. DOI: 10.1016/j.jmaa.2015.12.047

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Recommended Citation

D. Napoletani, D.C. Struppa, The stationary phase method for real analytic geometry, J. Math. Anal. Appl. (2016), http://dx.doi.org/10.1016/j.jmaa.2015.12.047

Peer Reviewed

1

Copyright

Elsevier

Creative Commons License

This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.