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Elementary integrals and the resolution of singularities of the phase

  • V. I. Arnold
  • S. M. Gusein-Zade
  • A. N. Varchenko
Chapter
Part of the Modern Birkhäuser Classics book series (MBC)

Abstract

In this chapter we shall study the asymptotics ofan oscillatory integral, the phase of which is a monomial. We shall indicate the connection between the asymptotics of an oscillatory integral and the poles of the meromorphic function \( F(\lambda)= \int f^{\lambda}(x)\phi(x) dx,\) where f is the phase, and \(\phi\)is the amplitude of the oscillatory integral.

Keywords

Asymptotic Expansion Analytic Continuation Meromorphic Function Irreducible Component Arithmetic Progression 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • V. I. Arnold
  • S. M. Gusein-Zade
    • 1
  • A. N. Varchenko
    • 2
  1. 1.Department of Mechanics and MathematicsMoscow State UniversityMoscowRussia
  2. 2.Department of MathematicsThe University of North Carolina at Chapel HillChapel HillUSA

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